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Wyświetlanie 1-15 z 19
Tytuł:
Extension maps in ultradifferentiable and ultraholomorphic function spaces
Autorzy:
Schmets, Jean
Valdivia, Manuel
Powiązania:
https://bibliotekanauki.pl/articles/1205776.pdf
Data publikacji:
2000
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
extension map
ultradifferentiable function
Roumieu type
Beurling type
Opis:
The problem of the existence of extension maps from 0 to ℝ in the setting of the classical ultradifferentiable function spaces has been solved by Petzsche [9] by proving a generalization of the Borel and Mityagin theorems for $C^{∞}$-spaces. We get a Ritt type improvement, i.e. from 0 to sectors of the Riemann surface of the function log for spaces of ultraholomorphic functions, by first establishing a generalization to some nonclassical ultradifferentiable function spaces.
Źródło:
Studia Mathematica; 2000, 143, 3; 221-250
0039-3223
Pojawia się w:
Studia Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the maximal function for rotation invariant measures in $ℝ^{n}$
Autorzy:
Vargas, Ana M.
Powiązania:
https://bibliotekanauki.pl/articles/1290316.pdf
Data publikacji:
1994
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
maximal operators
weak type estimates
Opis:
Given a positive measure μ in $ℝ^n$, there is a natural variant of the noncentered Hardy-Littlewood maximal operator $M_{μ}f(x) = sup_{x ∈ B} 1/μ(B) ʃ_{B} |f|dμ$, where the supremum is taken over all balls containing the point x. In this paper we restrict our attention to rotation invariant, strictly positive measures μ in $ℝ^n$. We give some necessary and sufficient conditions for $M_μ$ to be bounded from $L^{1}(dμ)$ to $L^{1,∞}(dμ)$.
Źródło:
Studia Mathematica; 1994, 110, 1; 9-17
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:
On non-primary Fréchet Schwartz spaces
Autorzy:
C. Díaz, J.
Powiązania:
https://bibliotekanauki.pl/articles/1218870.pdf
Data publikacji:
1997
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
Fréchet spaces
primary spaces
Schwartz spaces
unconditional decompositions
spaces of Moscatelli type
holomorphic functions of bounded type
Opis:
Let E be a Fréchet Schwartz space with a continuous norm and with a finite-dimensional decomposition, and let F be any infinite-dimensional subspace of E. It is proved that E can be written as G ⨁ H where G and H do not contain any subspace isomorphic to F. In particular, E is not primary. If the subspace F is not normable then the statement holds for other quasinormable Fréchet spaces, e.g., if E is a quasinormable and locally normable Köthe sequence space, or if E is a space of holomorphic functions of bounded type $ℋ_b(U)$, where U is a Banach space or a bounded absolutely convex open set in a Banach space.
Źródło:
Studia Mathematica; 1997, 126, 3; 291-307
0039-3223
Pojawia się w:
Studia Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Weak type (1,1) multipliers on LCA groups
Autorzy:
Raposo, José A
Powiązania:
https://bibliotekanauki.pl/articles/1220262.pdf
Data publikacji:
1997
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
weak type multipliers
maximal operators
vector inequalities
Opis:
In [ABB] Asmar, Berkson and Bourgain prove that for a sequence ${ϕ_j}^∞_{j=1} $ of weak type (1, 1) multipliers in $ℝ^n$ and a function $k ∈ L^1(ℝ^n)$ the weak type (1,1) constant of the maximal operator associated with ${k⁎ϕ_j}_j$ is controlled by that of the maximal operator associated with ${ϕ_j}_j$. In [ABG] this theorem is extended to LCA groups with an extra hypothesis: the multipliers must be continuous. In this paper we prove a more general version of this last result without assuming the continuity of the multipliers. The proof arises after simplifying the one in [ABB] which becomes then extensible to LCA groups.
Źródło:
Studia Mathematica; 1997, 122, 2; 123-130
0039-3223
Pojawia się w:
Studia Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Characterization of weak type by the entropy distribution of r-nuclear operators
Autorzy:
Defant, Martin
Junge, Marius
Powiązania:
https://bibliotekanauki.pl/articles/1292529.pdf
Data publikacji:
1993
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
entropy numbers
r-nuclear operators
weak type
Opis:
The dual of a Banach space X is of weak type p if and only if the entropy numbers of an r-nuclear operator with values in a Banach space of weak type q belong to the Lorentz sequence space $ℓ_{s,r}$ with 1/s + 1/p + 1/q = 1 + 1/r (0 < r < 1, 1 ≤ p, q ≤ 2). It is enough to test this for Y = X*. This extends results of Carl, König and Kühn.
Źródło:
Studia Mathematica; 1993, 107, 1; 1-14
0039-3223
Pojawia się w:
Studia Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
An inverse Sidon type inequality
Autorzy:
Fridli, S.
Powiązania:
https://bibliotekanauki.pl/articles/1292682.pdf
Data publikacji:
1993
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
Sidon type inequalities
Hardy spaces
convergence classes
Opis:
Sidon proved the inequality named after him in 1939. It is an upper estimate for the integral norm of a linear combination of trigonometric Dirichlet kernels expressed in terms of the coefficients. Since the estimate has many applications for instance in $L^1$ convergence problems and summation methods with respect to trigonometric series, newer and newer improvements of the original inequality has been proved by several authors. Most of them are invariant with respect to the rearrangement of the coefficients. Although the newest results are close to best possible, no nontrivial lower estimate has been given so far. The aim of this paper is to give the best rearrangement invariant function of coefficients that can be used in a Sidon type inequality. We also show that it is equivalent to an Orlicz type and a Hardy type norm. Examples of applications are also given.
Źródło:
Studia Mathematica; 1993, 105, 3; 283-308
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:
Pointwise multipliers on weighted BMO spaces
Autorzy:
Nakai, Eiichi
Powiązania:
https://bibliotekanauki.pl/articles/1219567.pdf
Data publikacji:
1997
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
multiplier
pointwise multiplier
bounded mean oscillation
space of homogeneous type
Opis:
Let E and F be spaces of real- or complex-valued functions defined on a set X. A real- or complex-valued function g defined on X is called a pointwise multiplier from E to F if the pointwise product fg belongs to F for each f ∈ E. We denote by PWM(E,F) the set of all pointwise multipliers from E to F. Let X be a space of homogeneous type in the sense of Coifman-Weiss. For 1 ≤ p < ∞ and for $ϕ: X×ℝ_{+} → ℝ_{+}$, we denote by $\text{bmo}_{ϕ,p}(X)$ the set of all functions $f ∈ L^{p}_{loc}(X)$ such that $\underset{a ∈ X, r>0}{\text{sup}} 1/{ϕ(a,r)} (1/μ(B(a,r)) \int_{B(a,r)} |f(x) -f_{B(a,r)}|^p dμ)^{1//p} < ∞$, where B(a,r) is the ball centered at a and of radius r, and $f_{B(a,r)}$ is the integral mean of f on B(a,r). Let $\text{bmo}_{ϕ}(X) =\text{bmo}_{ϕ,1}(X)$ and $\text{bmo}(X) = \text{bmo}_{1,1}(X)$. In this paper, we characterize $\text{PWM}(\text{bmo}_{ϕ1,p_1}(X), \text{bmo}_{ϕ2,p_2}(X))$. The following are examples of our results. $\text{PWM} (\text{bmo}_{(log(1//r))^{-α}}(\mathbb{T}^n), \text{bmo}_{(log(1//r))^{-β}}(\mathbb{T}^n)) = \text{bmo}_{(log(1//r))^{α-β-1}}(\mathbb{T}^n)$, 0≤β < α < 1, $\text{PWM} (\text{bmo}_{(log(1//r))^{-1}}(\mathbb{T}^n), \text{bmo} (\mathbb{T}^n)) = bmo_{(log log(1//r))^{-1}}(\mathbb{T}^n),$ $\text{PWM} (\text{bmo}(ℝ^n),\text{bmo}_{log(|a|+r+1//r),p}(ℝ^n)) = \text{bmo}(ℝ^n)$, 1 < p < ∞, etc.
Źródło:
Studia Mathematica; 1997, 125, 1; 35-56
0039-3223
Pojawia się w:
Studia Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On Báránys theorems of Carathéodory and Helly type
Autorzy:
Behrends, Ehrhard
Powiązania:
https://bibliotekanauki.pl/articles/1206023.pdf
Data publikacji:
2000
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
Krein-Milman theorem
Helly
Helly-type theorem
Bárány
Carathéodory
RNP
Opis:
The paper begins with a self-contained and short development of Bárány's theorems of Carathéodory and Helly type in finite-dimensional spaces together with some new variants. In the second half the possible generalizations of these results to arbitrary Banach spaces are investigated. The Carathéodory-Bárány theorem has a counterpart in arbitrary dimensions under suitable uniform compactness or uniform boundedness conditions. The proper generalization of the Helly-Bárány theorem reads as follows: if $C_{n}$, n=1,2,..., are families of closed convex sets in a bounded subset of a separable Banach space X such that there exists a positive $ε_{0}$ with $⋂_{C ∈ C_{n}} (C)_{ε} = ∅$ for $ε < ε_{0}$, then there are $C_{n} ∈ C_{n}$ with $⋂_{n} (C_{n})_{ε} = ∅$ for all $ε < ε_{0}$; here $(C)_{ε}$ denotes the collection of all x with distance at most ε to C.
Źródło:
Studia Mathematica; 2000, 141, 3; 235-250
0039-3223
Pojawia się w:
Studia Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Compactness of Hardy-type integral operators in weighted Banach function spaces
Autorzy:
E. Edmunds, David
Gurka, Petr
Pick, Luboš
Powiązania:
https://bibliotekanauki.pl/articles/1290637.pdf
Data publikacji:
1994
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
weighted Banach function space
Hardy-type operator
compact operator
Lorentz space
Opis:
We consider a generalized Hardy operator $Tf(x) = ϕ(x) ʃ_{0}^{x} ψfv$. For T to be bounded from a weighted Banach function space (X,v) into another, (Y,w), it is always necessary that the Muckenhoupt-type condition $ℬ = sup_{R>0} ∥ϕχ_{(R,∞)}∥_{Y}∥ψχ_{(0,R)}∥_{X'} < ∞$ be satisfied. We say that (X,Y) belongs to the category M(T) if this Muckenhoupt condition is also sufficient. We prove a general criterion for compactness of T from X to Y when (X,Y) ∈ M(T) and give an estimate for the distance of T from the finite rank operators. We apply the results to Lorentz spaces and characterize pairs of Lorentz spaces which fall into M (T).
Źródło:
Studia Mathematica; 1994, 109, 1; 73-90
0039-3223
Pojawia się w:
Studia Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
$B^q$ for parabolic measures
Autorzy:
Sweezy, Caroline
Powiązania:
https://bibliotekanauki.pl/articles/1217889.pdf
Data publikacji:
1998
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
parabolic-type measures
Lip (1,1/2) domain
good-λ inequalities
Opis:
If Ω is a Lip(1,1//2) domain, μ a doubling measure on $∂_{p}Ω, ∂//∂t - L_{i}$, i = 0,1, are two parabolic-type operators with coefficients bounded and measurable, 2 ≤ q < ∞, then the associated measures $ω_{0}$, $ω_{1}$ have the property that $ω_{0} ∈ B^{q}(μ)$ implies $ω_{1}$ is absolutely continuous with respect to $ω_{0}$ whenever a certain Carleson-type condition holds on the difference function of the coefficients of $L_{1}$ and $L_{0}$. Also $ω_{0} ∈ B^{q}(μ) $ implies $ω_{1} ∈ B^{q}(μ)$ whenever both measures are center-doubling measures. This is B. Dahlberg's result for elliptic measures extended to parabolic-type measures on time-varying domains. The method of proof is that of Fefferman, Kenig and Pipher.
Źródło:
Studia Mathematica; 1998, 131, 2; 115-135
0039-3223
Pojawia się w:
Studia Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Degenerate evolution problems and Beta-type operators
Autorzy:
Attalienti, Antonio
Campiti, Michele
Powiązania:
https://bibliotekanauki.pl/articles/1206074.pdf
Data publikacji:
2000
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
approximation process
$C_0$-semigroups of contractions
Beta-type operators
differential operators
Opis:
The present paper is concerned with the study of the differential operator Au(x):=α(x)u''(x)+β(x)u'(x) in the space C([0,1)] and of its adjoint Bv(x):=((αv)'(x)-β(x)v(x))' in the space $L^1(0,1)$, where α(x):=x(1-x)/2 (0≤x≤1). A careful analysis of their main properties is carried out in view of some generation results available in [6, 12, 20] and [25]. In addition, we introduce and study two different kinds of Beta-type operators as a generalization of similar operators defined in [18]. Among the corresponding approximation results, we show how they can be used in order to represent explicitly the solutions of the Cauchy problems associated with the operators A and Ã, where à is equal to B up to a suitable bounded additive perturbation.
Źródło:
Studia Mathematica; 2000, 140, 2; 117-139
0039-3223
Pojawia się w:
Studia Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Distribution and rearrangement estimates of the maximal function and interpolation
Autorzy:
U. Asekritova, Irina
Krugljak, Natan
Maligranda, Lech
Persson, Lars-Erik
Powiązania:
https://bibliotekanauki.pl/articles/1219812.pdf
Data publikacji:
1997
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
maximal functions
weights
weak type estimate
rearrangement
distribution functioni
inequalities
interpolation
K-functional
weighted spaces
Opis:
There are given necessary and sufficient conditions on a measure dμ(x)=w(x)dx under which the key estimates for the distribution and rearrangement of the maximal function due to Riesz, Wiener, Herz and Stein are valid. As a consequence, we obtain the equivalence of the Riesz and Wiener inequalities which seems to be new even for the Lebesgue measure. Our main tools are estimates of the distribution of the averaging function f** and a modified version of the Calderón-Zygmund decomposition. Analogous methods allow us to obtain K-functional formulas in terms of the maximal function for couples of weighted $L_p$-spaces.
Źródło:
Studia Mathematica; 1997, 124, 2; 107-132
0039-3223
Pojawia się w:
Studia Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Triebel-Lizorkin spaces on spaces of homogeneous type
Autorzy:
Han, Y.-S
Powiązania:
https://bibliotekanauki.pl/articles/1290774.pdf
Data publikacji:
1994
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
spaces of homogeneous type
$H^p$ and Triebel-Lizorkin spaces
Littlewood-Paley S-function
atomic decomposition
Opis:
In [HS] the Besov and Triebel-Lizorkin spaces on spaces of homogeneous type were introduced. In this paper, the Triebel-Lizorkin spaces on spaces of homogeneous type are generalized to the case where $p_0 < p ≤ 1 ≤ q < ∞$, and a new atomic decomposition for these spaces is obtained. As a consequence, we give the Littlewood-Paley characterization of Hardy spaces on spaces of homogeneous type which were introduced by the maximal function characterization in [MS2].
Źródło:
Studia Mathematica; 1994, 108, 3; 247-273
0039-3223
Pojawia się w:
Studia Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 19

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