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    Wyświetlanie 1-15 z 15
    Tytuł:
    Spaces defined by the level function and their duals
    Autorzy:
    Sinnamon, Gord
    Powiązania:
    https://bibliotekanauki.pl/articles/1290183.pdf
    Data publikacji:
    1994
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    function spaces
    Hölder's inequality
    Hardy's inequality
    dual spaces
    Opis:
    The classical level function construction of Halperin and Lorentz is extended to Lebesgue spaces with general measures. The construction is also carried farther. In particular, the level function is considered as a monotone map on its natural domain, a superspace of $L^p$. These domains are shown to be Banach spaces which, although closely tied to $L^p$ spaces, are not reflexive. A related construction is given which characterizes their dual spaces.
    Źródło:
    Studia Mathematica; 1994, 111, 1; 19-52
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On sharp reiteration theorems and weighted norm inequalities
    Autorzy:
    Bastero, Jesús
    Milman, Mario
    Ruiz, Francisco
    Powiązania:
    https://bibliotekanauki.pl/articles/1206002.pdf
    Data publikacji:
    2000
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    reiteration
    weights
    Hardy inequality
    Opis:
    We prove sharp end forms of Holmstedt's reiteration theorem which are closely connected with a general form of Gehring's Lemma. Reverse type conditions for the Hardy-Littlewood-Pólya order are considered and the maximal elements are shown to satisfy generalized Gehring conditions. The methods we use are elementary and based on variants of reverse Hardy inequalities for monotone functions.
    Źródło:
    Studia Mathematica; 2000, 142, 1; 7-24
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Mosers Inequality for a class of integral operators
    Autorzy:
    Holland, Finbarr
    Walsh, David
    Powiązania:
    https://bibliotekanauki.pl/articles/1289652.pdf
    Data publikacji:
    1995
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    Moser's Inequality
    integral operator
    distribution function
    Opis:
    Let 1 < p < ∞, q = p/(p-1) and for $f ∈ L^p(0,∞)$ define $F(x) = (1/x) ʃ_0^x f(t)dt$, x > 0. Moser's Inequality states that there is a constant $C_p$ such that $sup_{a≤1} sup_{f∈B_{p}} ʃ_{0}^{∞} exp[ax^{q}|F(x)|^{q} - x]dx= C_p$ where $B_p$ is the unit ball of $L^p$. Moreover, the value a = 1 is sharp. We observe that $F = K_1$ f where the integral operator $K_1$ has a simple kernel K. We consider the question of for what kernels K(t,x), 0 ≤ t, x < ∞, this result can be extended, and proceed to discuss this when K is non-negative and homogeneous of degree -1. A sufficient condition on K is found for the analogue of Moser's Inequality to hold. An internal constant ψ, the counterpart of the constant a, arises naturally. We give a condition on K that ψ be sharp. Some applications are discussed.
    Źródło:
    Studia Mathematica; 1995, 113, 2; 141-168
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Two-weight norm inequalities for maximal functions on homogeneous spaces and boundary estimates
    Autorzy:
    Luís Zani, Sérgio
    Powiązania:
    https://bibliotekanauki.pl/articles/1219073.pdf
    Data publikacji:
    1997
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    norm inequality
    weight
    maximal function
    homogeneous space
    Opis:
    Let D be an open subset of a homogeneous space(X,d,μ). Consider the maximal function $M_φ f(x) = sup1/φ(B) ʃ_{B∩∂D} |f|dν$, x∈ D, where the supremum is taken over all balls of the form B = B(a(x),r) with r > t(x) = d(x,∂D), a(x)∈ ∂D is such that d(a(x),x) < 3/2 t(x)$ and φ is a nonnegative set function defined for all Borel sets of X satisfying the quasi-monotonicity and doubling properties. We give a necessary and sufficient condition on the weights w and v for the weighted norm inequality (0.1) $(ʃ_D [M_φ(f)]^q wdμ)^{1/q} ≤ c(ʃ_{∂D} |f|^p vdν)^{1/p}$ to hold when 1 < p < q < ∞, $σdν = v^{1-p'}dν$ is a doubling weight, and dν is a doubling measure, and give a sufficient condition for (0.1) when 1 < p ≤ q < ∞ without assuming that σ is a doubling weight but with an extra assumption on φ. Another characterization for (0.1) is also provided for 1 < p ≤ q < ∞ and D of the form Y×(0,∞), where Y is a homogeneous space with group structure. These results generalize some known theorems in the case when $M_φ$ is the fractional maximal function in $ℝ^{n+1}_+$, that is, when $M_φ f(x,t) = M_γ f(x,t) = sup_{r>t} 1/(ν(B(x,r))^{1-γ}) ʃ_{B(x,r)} |f|dν$, where $(x,t) ∈ ℝ^{n+1}_+$, 0 < γ < 1, and ν is a doubling measure in $ℝ^n$.
    Źródło:
    Studia Mathematica; 1997, 126, 1; 67-94
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    $L^p$ weighted inequalities for the dyadic square function
    Autorzy:
    Uchiyama, Akihito
    Powiązania:
    https://bibliotekanauki.pl/articles/1289002.pdf
    Data publikacji:
    1995
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    dyadic square function
    dyadic maximal function
    weighted inequality
    Opis:
    We prove that $ʃ(S_df)^pVdx ≤ C_{p,n}ʃ |f|^p M_d^{([p/2]+2)}Vdx$, where $S_d$ is the dyadic square function, $M_d^{(k)}$ is the k-fold application of the dyadic Hardy-Littlewood maximal function and p > 2.
    Źródło:
    Studia Mathematica; 1995, 115, 2; 135-149
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The converse of the Hölder inequality and its generalizations
    Autorzy:
    Matkowski, Janusz
    Powiązania:
    https://bibliotekanauki.pl/articles/1290537.pdf
    Data publikacji:
    1994
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    measure space
    integrable step functions
    conjugate functions
    a converse of Hölder inequality
    subadditive function
    convex function
    generalized Hölder-Minkowski inequality
    Opis:
    Let (Ω,Σ,μ) be a measure space with two sets A,B ∈ Σ such that 0 < μ (A) < 1 < μ (B) < ∞ and suppose that ϕ and ψ are arbitrary bijections of [0,∞) such that ϕ(0) = ψ(0) = 0. The main result says that if $ʃ_Ω xydμ ≤ ϕ^{-1} (\int_{Ω} ϕ∘x dμ) ψ^{-1} (\int_{Ω} ψ∘x dμ)$ for all μ-integrable nonnegative step functions x,y then ϕ and ψ must be conjugate power functions. If the measure space (Ω,Σ,μ) has one of the following properties: (a) μ (A) ≤ 1 for every A ∈ Σ of finite measure; (b) μ (A) ≥ 1 for every A ∈ Σ of positive measure, then there exist some broad classes of nonpower bijections ϕ and ψ such that the above inequality holds true. A general inequality which contains integral Hölder and Minkowski inequalities as very special cases is also given.
    Źródło:
    Studia Mathematica; 1994, 109, 2; 171-182
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Weighted inequalities for monotone and concave functions
    Autorzy:
    Heinig, Hans
    Maligranda, Lech
    Powiązania:
    https://bibliotekanauki.pl/articles/1388599.pdf
    Data publikacji:
    1995
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    weighted integral inequalities
    weighted Hardy inequalities
    weighted Hardy inequalities for monotone functions
    weighted Favard-Berwald inequality
    reverse Hölder inequality
    concave functions
    Opis:
    Characterizations of weight functions are given for which integral inequalities of monotone and concave functions are satisfied. The constants in these inequalities are sharp and in the case of concave functions, constitute weighted forms of Favard-Berwald inequalities on finite and infinite intervals. Related inequalities, some of Hardy type, are also given.
    Źródło:
    Studia Mathematica; 1995, 116, 2; 133-165
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Weak type estimates for operators of potential type
    Autorzy:
    Wheeden, Richard L.
    Zhao, Shiying
    Powiązania:
    https://bibliotekanauki.pl/articles/1287570.pdf
    Data publikacji:
    1996
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    norm inequality
    weight
    operator of potential type
    homogeneous space
    Opis:
    We derive two-weight weak type estimates for operators of potential type in homogeneous spaces. The conditions imposed on the weights are testing conditions of the kind first studied by E. T. Sawyer [4]. We also give some applications to strong type estimates as well as to operators on half-spaces.
    Źródło:
    Studia Mathematica; 1996, 119, 2; 149-160
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The one-sided minimal operator and the one-sided reverse Holder inequality
    Autorzy:
    Cruz-Uribe, David
    Neugebauer, C.
    Olesen, V.
    Powiązania:
    https://bibliotekanauki.pl/articles/1288722.pdf
    Data publikacji:
    1995
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    one-sided (A_p) weights
    reverse Hölder inequality
    minimal function
    Opis:
    We introduce the one-sided minimal operator, $m^+f$, which is analogous to the one-sided maximal operator. We determine the weight classes which govern its two-weight, strong and weak-type norm inequalities, and show that these two classes are the same. Then in the one-weight case we use this class to introduce a new one-sided reverse Hölder inequality which has several applications to one-sided $(A^+_p)$ weights.
    Źródło:
    Studia Mathematica; 1995, 116, 3; 255-270
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A variant sharp estimate for multilinear singular integral operators
    Autorzy:
    Hu, Guoen
    Yang, Dachun
    Powiązania:
    https://bibliotekanauki.pl/articles/1206036.pdf
    Data publikacji:
    2000
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    multilinear singular integral operator
    BMO
    weighted norm inequality
    sharp estimate
    Opis:
    We establish a variant sharp estimate for multilinear singular integral operators. As applications, we obtain the weighted norm inequalities on general weights and certain $Llog^{+}L$ type estimates for these multilinear operators.
    Źródło:
    Studia Mathematica; 2000, 141, 1; 25-22
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A Carlson type inequality with blocks and interpolation
    Autorzy:
    Ya Kruglyak, Natan
    Maligranda, Lech
    Persson, Lars
    Powiązania:
    https://bibliotekanauki.pl/articles/1292922.pdf
    Data publikacji:
    1993
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    concavity
    Carlson's inequality
    blocks
    interpolation
    Peetre's interpolation functor
    Calderón-Lozanovskiǐ construction
    Opis:
    An inequality, which generalizes and unifies some recently proved Carlson type inequalities, is proved. The inequality contains a certain number of "blocks" and it is shown that these blocks are, in a sense, optimal and cannot be removed or essentially changed. The proof is based on a special equivalent representation of a concave function (see [6, pp. 320-325]). Our Carlson type inequality is used to characterize Peetre's interpolation functor $⟨⟩_{φ}$ (see [26]) and its Gagliardo closure on couples of functional Banach lattices in terms of the Calderón-Lozanovskiǐ construction. Our interest in this functor is inspired by the fact that if $φ = t^{θ}(0 < θ < 1)$, then, on couples of Banach lattices and their retracts, it coincides with the complex method (see [20], [27]) and, thus, it may be regarded as a "real version" of the complex method.
    Źródło:
    Studia Mathematica; 1993, 104, 2; 161-180
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Strong convergence theorems for two-parameter Walsh-Fourier and trigonometric-Fourier series
    Autorzy:
    Weisz, Ferenc
    Powiązania:
    https://bibliotekanauki.pl/articles/1288490.pdf
    Data publikacji:
    1996
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    martingale and classical Hardy spaces
    p-atom
    atomic decomposition
    Walsh functions
    Hardy-Littlewood inequality
    Opis:
    The martingale Hardy space $H_p([0,1)^2)$ and the classical Hardy space $H_p(^2)$ are introduced. We prove that certain means of the partial sums of the two-parameter Walsh-Fourier and trigonometric-Fourier series are uniformly bounded operators from $H_p$ to $L_p$ (0 < p ≤ 1). As a consequence we obtain strong convergence theorems for the partial sums. The classical Hardy-Littlewood inequality is extended to two-parameter Walsh-Fourier and trigonometric-Fourier coefficients. The dual inequalities are also verified and a Marcinkiewicz-Zygmund type inequality is obtained for BMO spaces.
    Źródło:
    Studia Mathematica; 1995-1996, 117, 2; 173-194
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Hardy type inequalities for two-parameter Vilenkin-Fourier coefficients
    Autorzy:
    Simon, Péter
    Weisz, Ferenc
    Powiązania:
    https://bibliotekanauki.pl/articles/1219101.pdf
    Data publikacji:
    1997
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    two-parameter martingales and Hardy spaces
    rectangle p-atoms
    Vilenkin functions
    Hardy-Littlewood inequality
    Opis:
    Our main result is a Hardy type inequality with respect to the two-parameter Vilenkin system (*) $(∑_{k=1}^∞ ∑_{j=1}^∞ |f̂(k,j)|^{p}(kj)^{p-2})^{1/p} ≤ C_p∥f∥_{H^p_{**}}$ (1/2 < p≤2) where f belongs to the Hardy space $H_{**}^p (G_m × G_s)$ defined by means of a maximal function. This inequality is extended to p > 2 if the Vilenkin-Fourier coefficients of f form a monotone sequence. We show that the converse of (*) also holds for all p > 0 under the monotonicity assumption.
    Źródło:
    Studia Mathematica; 1997, 125, 3; 231-246
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Double exponential integrability, Bessel potentials and embedding theorems
    Autorzy:
    Edmunds, David E.
    Gurka, Petr
    Opic, Bohumír
    Powiązania:
    https://bibliotekanauki.pl/articles/1289003.pdf
    Data publikacji:
    1995
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    Bessel potential
    Riesz potential, generalized Lorentz-Zygmund spaces
    exponential integrability
    Hardy inequality
    Orlicz spaces
    Bessel potential spaces
    Opis:
    This paper is a continuation of [5] and provides necessary and sufficient conditions for double exponential integrability of the Bessel potential of functions from suitable (generalized) Lorentz-Zygmund spaces. These results are used to establish embedding theorems for Bessel potential spaces which extend Trudinger's result.
    Źródło:
    Studia Mathematica; 1995, 115, 2; 151-181
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the exponential Orlicz norms of stopped Brownian motion
    Autorzy:
    Peškir, Goran
    Powiązania:
    https://bibliotekanauki.pl/articles/1288072.pdf
    Data publikacji:
    1996
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    Brownian motion (Wiener process)
    stopping time
    exponential Young function
    exponential Orlicz norm
    Doob's maximal inequality for martingales
    Burkholder-Gundy's inequality
    Davis' best constants
    Hermite polynomial
    continuous (local) martingale
    Ito's integral
    the quadratic variation process
    time change (of Brownian motion)
    Kahane-Khinchin's inequalities
    Opis:
    Necessary and sufficient conditions are found for the exponential Orlicz norm (generated by $ψ_p(x) = exp(|x|^p)-1$ with 0 < p ≤ 2) of $max_{0≤t≤τ}|B_t|$ or $|B_τ|$ to be finite, where $B = (B_t)_{t≥0}$ is a standard Brownian motion and τ is a stopping time for B. The conditions are in terms of the moments of the stopping time τ. For instance, we find that $∥max_{0≤t≤τ}|B_t|∥_{ψ_1} < ∞$ as soon as $E(τ^{k}) = O(C^{k}k^{k})$ for some constant C > 0 as k → ∞ (or equivalently $∥τ∥_{ψ_1} < ∞$). In particular, if τ ∼ Exp(λ) or $|N(0,σ^2)|$ then the last condition is satisfied, and we obtain $∥max_{0≤t≤τ}|B_t|∥_{ψ_1} ≤ K √{E(τ)}$ with some universal constant K > 0. Moreover, this inequality remains valid for any class of stopping times τ for B satisfying $E(τ^{k}) ≤ C(Eτ)^{k}k^{k}$ for all k ≥ 1 with some fixed constant C > 0. The method of proof relies upon Taylor expansion, Burkholder-Gundy's inequality, best constants in Doob's maximal inequality, Davis' best constants in the $L^p$-inequalities for stopped Brownian motion, and estimates of the smallest and largest positive zero of Hermite polynomials. The results extend to the case of any continuous local martingale (by applying the time change method of Dubins and Schwarz).
    Źródło:
    Studia Mathematica; 1995-1996, 117, 3; 253-273
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-15 z 15

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