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1
Content available remote Discrete Hardy spaces
100%
Boza S. , Carro M. J.
Studia Mathematica
|
1998
|
tom 129
|
nr 1
31-50
EN
We study various characterizations of the Hardy spaces $H^p(ℤ)$ via the discrete Hilbert transform and via maximal and square functions. Finally, we present the equivalence with the classical atomic characterization of $H^p(ℤ)$ given by Coifman and Weiss in [CW]. Our proofs are based on some results concerning functions of exponential type.
2
Content available remote Weak martingale hardy spaces
100%
Weisz F.
Probability and Mathematical Statistics
|
1998
|
tom Vol. 18, Fasc. 1
133--148
EN
Weak martingale Hardy spaces generated by an operator T are investigated. The concept of weak atoms is introduced and an atomic decomposition of the space wHTp is given if the operator T is predictable. Martingale inequalities between weak Hardy spaces generated by two different operators are considered. In particular, we obtain inequalities for the maximal function, for the q-variation, and for the conditional q-variation. The duals of the weak Hardy spaces generated by these special operators are characterized.
3
Content available remote Local Hardy spaces on Chébli-Trimèche hypergroups
100%
Bloom W. R. , Xu Z.
Studia Mathematica
|
1999
|
tom 133
|
nr 3
197-230
EN
We investigate the local Hardy spaces $h^p$ on Chébli-Trimèche hypergroups, and establish the equivalence of various characterizations of these in terms of maximal functions and atomic decomposition.
4
Content available Hilbert-Schmidtness of weighted composition operators and their differences on Hardy spaces
100%
Lo C.-o. , Loh A. W.-k.
Opuscula Mathematica
|
2020
|
tom Vol. 40, no. 4
495--507
EN
Let u and φ be two analytic functions on the unit disk D such that φ (D) ⊂ D. A weighted composition operator uCφ induced by u and φ is defined on H2, the Hardy space of D, by [formula] for every ∫ in H2. We obtain sufficient conditions for Hilbert-Schmidtness of v,Cv on H2 in terms of function-theoretic properties of u and φ. Moreover, we characterize Hilbert-Schmidt difference of two weighted composition operators on H2.
5
Content available remote Two-parameter Hardy-Littlewood inequalities
100%
Weisz F.
Studia Mathematica
|
1996
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tom 118
|
nr 2
175-184
EN
The inequality (*) $(∑_{|n|=1}^{∞} ∑_{|m|=1}^{∞} |nm|^{p-2} |f̂(n,m)|^p)^{1/p} ≤ C_p ∥ƒ∥_{H_p}$ (0 < p ≤ 2) is proved for two-parameter trigonometric-Fourier coefficients and for the two-dimensional classical Hardy space $H_p$ on the bidisc. The inequality (*) is extended to each p if the Fourier coefficients are monotone. For monotone coefficients and for every p, the supremum of the partial sums of the Fourier series is in $L_p$ whenever the left hand side of (*) is finite. From this it follows that under the same condition the two-dimensional trigonometric-Fourier series of an arbitrary function from $H_1$ converges a.e. and also in $L_1$ norm to that function.
6
Content available remote Harmonic functions and Hardy spaces on trees with boundaries
100%
Pytlik T.
Colloquium Mathematicum
|
1992
|
tom 63
|
nr 2
263-272
7
Content available remote Multipliers of sequence spaces
100%
Cheng R. , Mashreghi J. , Ross W. T.
Concrete Operators
|
2017
|
tom 4
|
nr 1
76-108
EN
This paper is selective survey on the space lAp and its multipliers. It also includes some connections of multipliers to Birkhoff-James orthogonality
8
Content available remote Convolution operators on Hardy spaces
100%
Lin C.-C.
Studia Mathematica
|
1996
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tom 120
|
nr 1
53-59
EN
We give sufficient conditions on the kernel K for the convolution operator Tf = K ∗ f to be bounded on Hardy spaces $H^p(G)$, where G is a homogeneous group.
9
Certain multiplier results on Bp spaces
100%
Naik S.
Journal of Applied Analysis
|
2023
|
tom Vol. 29, nr 1
91--98
EN
In this article, we use a particular case of convolution as an operator to discuss a number of problems concerning multiplier results between function spaces such as Hardy and Bp-spaces. As a consequence, we extend certain well-known results on fractional derivatives and fractional integrals. Also, we find condition on the parameters b, c such that Pb,c in Bp.
10
Content available remote An inverse Sidon type inequality
100%
Fridli S.
Studia Mathematica
|
1993
|
tom 105
|
nr 3
283-308
EN
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.
11
Content available remote On Hardy spaces on worm domains
100%
Monguzzi A.
Concrete Operators
|
2016
|
tom 3
|
nr 1
29-42
EN
In this review article we present the problem of studying Hardy spaces and the related Szeg˝o projection on worm domains. We review the importance of the Diederich–Fornæss worm domain as a smooth bounded pseudoconvex domain whose Bergman projection does not preserve Sobolev spaces of sufficiently high order and we highlight which difficulties arise in studying the same problem for the Szeg˝o projection. Finally, we announce and discuss the results we have obtained so far in the setting of non-smooth worm domains.
12
Content available remote Subnormal operators of Hardy type
100%
Rudol K.
Banach Center Publications
|
1997
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tom 38
|
nr 1
315-324
13
Content available remote Harmonic functions on the real hyperbolic ball I: Boundary values and atomic decomposition of Hardy spaces
88%
Jaming P.
Colloquium Mathematicum
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1999
|
tom 80
|
nr 1
63-82
EN
We study harmonic functions for the Laplace-𝔹eltrami operator on the real hyperbolic space $𝔹_n$. We obtain necessary and sufficient conditions for these functions and their normal derivatives to have a boundary distribution. In doing so, we consider different behaviors of hyperbolic harmonic functions according to the parity of the dimension of the hyperbolic ball $𝔹_n$. We then study the Hardy spaces $H^p(𝔹_n)$, 0
14
Content available remote $(H_p,L_p)$-type inequalities for the two-dimensional dyadic derivative
88%
Weisz F.
Studia Mathematica
|
1996
|
tom 120
|
nr 3
271-288
EN
It is shown that the restricted maximal operator of the two-dimensional dyadic derivative of the dyadic integral is bounded from the two-dimensional dyadic Hardy-Lorentz space $H_{p,q}$ to $L_{p,q}$ (2/3 < p < ∞, 0 < q ≤ ∞) and is of weak type $(L_1,L_1)$. As a consequence we show that the dyadic integral of a ∞ function $f ∈ L_1$ is dyadically differentiable and its derivative is f a.e.
15
Content available remote Essential spectra of weighted composition operators with hyperbolic symbols
88%
Hyvärinen O. , Nieminen I.
Concrete Operators
|
2015
|
tom 2
|
nr 1
EN
In this paperwe study both the spectra and the essential spectra ofweighted composition operators on Hardy spaces Hp(ⅅ), standard weighted Bergman spaces Apα(ⅅ) and weighted H∞1-type spaces when the symbols are of hyperbolic type
16
Content available remote Fejér means of two-dimensional Fourier transforms on $H_p(ℝ × ℝ)$
88%
Weisz F.
Colloquium Mathematicum
|
1999
|
tom 82
|
nr 2
155-166
EN
The two-dimensional classical Hardy spaces $H_p(ℝ × ℝ)$ are introduced and it is shown that the maximal operator of the Fejér means of a tempered distribution is bounded from $H_p(ℝ × ℝ)$ to $L_p(ℝ^2)$ (1/2 < p ≤ ∞) and is of weak type $(H^{#}_1 (ℝ × ℝ), L_1(ℝ^2))$ where the Hardy space $H^#_1(ℝ × ℝ)$ is defined by the hybrid maximal function. As a consequence we deduce that the Fejér means of a function f ∈ $H_1^#(ℝ × ℝ)$ ⊃ $LlogL(ℝ^2)$ converge to f a.e. Moreover, we prove that the Fejér means are uniformly bounded on $H_p(ℝ × ℝ)$ whenever 1/2 < p < ∞. Thus, in case f ∈ $H_p(ℝ × ℝ)$, the Fejér means converge to f in $H_p(ℝ × ℝ)$ norm (1/2 < p < ∞). The same results are proved for the conjugate Fejér means.
17
Content available remote A Riemann-Hilbert problem with a vanishing coefficient and applications to Toeplitz operators
88%
Perälä A. , Virtanen J. A. , Wolf L.
Concrete Operators
|
2013
|
tom 1
28-36
EN
We study the homogeneous Riemann-Hilbert problem with a vanishing scalar-valued continuous coefficient. We characterize non-existence of nontrivial solutions in the case where the coefficient has its values along several rays starting from the origin. As a consequence, some results on injectivity and existence of eigenvalues of Toeplitz operators in Hardy spaces are obtained.
18
Content available remote Weighted composition operators via Berezin transform and Carleson measure
75%
Kumar R. , Singh K. J.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
|
2006
|
tom Vol. 46, [Z] 1
63-78
EN
In this paper, we study the boundedness and the compactness of weighted composition operators on Hardy spaces and weighted Bergman spaces of the unit polydisc in C^n.
19
Content available Weighted composition operators via Berezin transform and Carleson measure
75%
Kumar R. , Singh K. J.
Commentationes Mathematicae
|
2006
|
tom 46
|
nr 1
EN
In this paper, we study the boundedness and the compactness of weighted composition operators on Hardy spaces and weighted Bergman spaces of the unit polydisc in \(\mathbf{C}^n\).
20
Content available remote Riesz means of Fourier transforms and Fourier series on Hardy spaces
75%
Weisz F.
Studia Mathematica
|
1998
|
tom 131
|
nr 3
253-270
EN
Elementary estimates for the Riesz kernel and for its derivative are given. Using these we show that the maximal operator of the Riesz means of a tempered distribution is bounded from $H_p(ℝ)$ to $L_p(ℝ)$ (1/(α+1) < p < ∞) and is of weak type (1,1), where $H_p(ℝ)$ is the classical Hardy space. As a consequence we deduce that the Riesz means of a function $⨍ ∈ L_1(ℝ)$ converge a.e. to ⨍. Moreover, we prove that the Riesz means are uniformly bounded on $H_p(ℝ)$ whenever 1/(α+1) < p < ∞. Thus, in case $⨍ ∈ H_p(ℝ)$, the Riesz means converge to ⨍ in $H_p(ℝ)$ norm (1/(α+1) < p < ∞). The same results are proved for the conjugate Riesz means and for Fourier series of distributions.
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