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    Wyświetlanie 1-9 z 9
    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:
    On a converse inequality for maximal functions in Orlicz spaces
    Autorzy:
    Kita, H.
    Powiązania:
    https://bibliotekanauki.pl/articles/1287708.pdf
    Data publikacji:
    1996
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    Hardy-Littlewood maximal function
    Orlicz space
    Opis:
    Let $Φ(t) = ʃ_{0}^{t} a(s)ds$ and $Ψ(t) = ʃ_{0}^{t} b(s)ds$, where a(s) is a positive continuous function such that $ʃ_{1}^{∞} a(s)/s ds = ∞$ and b(s) is quasi-increasing and $lim_{s→∞}b(s) = ∞$. Then the following statements for the Hardy-Littlewood maximal function Mf(x) are equivalent: (j) there exist positive constants $c_1$ and $s_{0}$ such that $ʃ_{1}^{s} a(t)/t dt ≥ c_{1}b(c_{1}s)$ for all $s ≥ s_{0}$; (jj) there exist positive constants $c_2$ and $c_3$ such that $ʃ_{0}^{2π} Ψ((c_2)/(|⨍|_{}) |⨍(x)|) dx ≤ c_3 + c_{3} ʃ_{0}^{2π} Φ(1/(|⨍|_{})) Mf(x) dx$ for all $⨍ ∈ L^{1}()$.
    Źródło:
    Studia Mathematica; 1996, 118, 1; 1-10
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On convergence for the square root of the Poisson kernel in symmetric spaces of rank 1
    Autorzy:
    Rönning, Jan-Olav
    Powiązania:
    https://bibliotekanauki.pl/articles/1219076.pdf
    Data publikacji:
    1997
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    maximal function
    square root of the Poisson kernel
    convergence region
    symmetric space of rank 1
    Opis:
    Let P(z,β) be the Poisson kernel in the unit disk , and let $P_{λ}f(z) = ʃ_{∂} P(z,φ)^{1//2+λ} f(φ)dφ$ be the λ -Poisson integral of f, where $f ∈ L^p(∂)$. We let $P_{λ}f$ be the normalization $P_{λ}f//P_{λ}1$. If λ >0, we know that the best (regular) regions where $P_{λ}f$ converges to f for a.a. points on ∂ are of nontangential type. If λ =0 the situation is different. In a previous paper, we proved a result concerning the convergence of $P_0f$ toward f in an $L^p$ weakly tangential region, if $f ∈ L^p(∂)$ and p > 1. In the present paper we will extend the result to symmetric spaces X of rank 1. Let f be an $L^p$ function on the maximal distinguished boundary K/M of X. Then $P_{0}f(x)$ will converge to f(kM) as x tends to kM in an $L^p$ weakly tangential region, for a.a. kM ∈ K/M.
    Źródło:
    Studia Mathematica; 1997, 125, 3; 219-229
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the construction of the common optimal market index in the Sharpe model
    Autorzy:
    Kuryłek, W.
    Powiązania:
    https://bibliotekanauki.pl/articles/205979.pdf
    Data publikacji:
    1999
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    regresja liniowa
    zastosowanie teorii systemów w ekonomii
    investment
    linear regression
    loss function
    market index
    maximal eigenvalue
    portfolio analysis
    principal components
    rates of return
    Sharpe model
    stock markets
    Opis:
    The purpose of this paper is to determine one factor which represents the whole market behavior on the basis of the rates of return of all equities traded oo this market. In the seminaal Sharpe model the factor is an exogenous varialble which is not determined by the model itself. This paper extends Sharpe's idea, as it assumes that the factor is a linear combination of all the rates of return of all traded equities. To determine this coefiicients of this linear combination we minimize the loss function which expresses the weighted mean square deviation of all rates of return from their predictions, having given the linear combination form of the market index. It is found that the vector of linear coeffcients has to be a nonzero eigenvector associated with the maximal eigenvalue of the appropriately transformed and estimated covariance matrix. The optimal market index for the Warsaw Stock Exchange was compared with the standard index. It occurs that there is only a very small difference between the standard index of this market and the optimal index.
    Źródło:
    Control and Cybernetics; 1999, 28, 4; 779-787
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    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
    Tytuł:
    Pointwise multipliers for reverse Holder spaces
    Autorzy:
    M. Buckley, Stephen
    Powiązania:
    https://bibliotekanauki.pl/articles/1290583.pdf
    Data publikacji:
    1994
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    reverse Hölder condition
    maximal function
    weight
    doubling measure
    Opis:
    We classify weights which map reverse Hölder weight spaces to other reverse Hölder weight spaces under pointwise multiplication. We also give some fairly general examples of weights satisfying weak reverse Hölder conditions.
    Źródło:
    Studia Mathematica; 1994, 109, 1; 23-39
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Two-weight mixed ф-inequalities for the one-sided maximal function
    Autorzy:
    Lai, Qinsheng
    Powiązania:
    https://bibliotekanauki.pl/articles/1289097.pdf
    Data publikacji:
    1995
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    Young function
    one-sided maximal function
    Fefferman-Stein type fractional operator
    Hardy-type operator
    Opis:
    Suppose u, v, w, and t are weight functions on an appropriate measure space (X,μ), and $Φ_1$, $Φ_2$ are Young functions satisfying a certain relationship. Let T denote an operator to be specified below. The main purpose of this paper is to characterize (i) the strong type mixed Φ-inequality $Φ^{-1}_{2}(ʃ_{X} Φ_{2}(T(fv))wdμ) ≤ Φ^{-1}_{1} (ʃ_X Φ_{1}(Cf)vdμ)$, (ii) the weak type mixed Φ-inequality $Φ^{-1}_2 (ʃ_{|Tf|>λ}$ Φ_{2}(λw)tdμ) ≤ Φ^{-1}_{1} (ʃ_{X} Φ_{1}(Cfu)vdμ)$ and (iii) the extra-weak type mixed Φ-inequality $|{x ∈ X : |Tf(x)| > λ}|_{wdμ} ≤ Φ_{2}Φ^{-1}_{1} (ʃ_{X} Φ_{1}(Cfu/λ)vdμ)$, when T is the one-sided maximal function $M^{+}_{g}$; as well to characterize (iii) for the Fefferman-Stein type fractional maximal operator and the Hardy-type operator.
    Źródło:
    Studia Mathematica; 1995, 115, 1; 1-22
    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:
    Universal images of universal elements
    Autorzy:
    Bernal-González, Luis
    Powiązania:
    https://bibliotekanauki.pl/articles/1206133.pdf
    Data publikacji:
    2000
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    universal element
    almost commutativity
    universal image
    dense range
    dense hypercyclic manifold
    point spectrum of the adjoint
    analytic function of an operator
    real entire function
    maximal dimension
    Opis:
    We furnish several necessary and sufficient conditions for the following property: For a topological space X, a continuous selfmapping S of X and a family τ of continuous selfmappings of X, the image under S of every τ-universal element is also τ-universal. An application in operator theory, where we extend results of Bourdon, Herrero, Bes, Herzog and Lemmert, is given. In particular, it is proved that every hypercyclic operator on a real or complex Banach space has a dense invariant linear manifold with maximal algebraic dimension consisting, apart from zero, of vectors which are hypercyclic.
    Źródło:
    Studia Mathematica; 2000, 138, 3; 241-250
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-9 z 9

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