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1
Content available remote

Convolution operators on Hardy spaces

100%
Lin C.-C.
Studia Mathematica
|
1996
|
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.
2
Content available remote

Two-parameter Hardy-Littlewood inequalities

100%
Weisz F.
Studia Mathematica
|
1996
|
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.
3
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.
4
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
5
Content available remote

Subnormal operators of Hardy type

100%
Rudol K.
Banach Center Publications
|
1997
|
tom 38
|
nr 1
315-324
6
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.
7
Content available remote

Harmonic functions and Hardy spaces on trees with boundaries

100%
Pytlik T.
Colloquium Mathematicum
|
1992
|
tom 63
|
nr 2
263-272
8
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.
9
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.
10
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A Riemann-Hilbert problem with a vanishing coefficient and applications to Toeplitz operators

88%
Perälä A., Virtanen J. A., Wolf L.
Concrete Operators
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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.
11
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
12
Content available remote

Harmonic functions on the real hyperbolic ball I: Boundary values and atomic decomposition of Hardy spaces

88%
Jaming P.
Colloquium Mathematicum
|
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
13
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.
14
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.
15
Content available remote

Order bounded composition operators on the Hardy spaces and the Nevanlinna class

75%
Jaoua N.
Studia Mathematica
|
1999
|
tom 134
|
nr 1
35-55
EN
We study the order boundedness of composition operators induced by holomorphic self-maps of the open unit disc D. We consider these operators first on the Hardy spaces $H^p$ 0 < p < ∞ and then on the Nevanlinna class N. Given a non-negative increasing function h on [0,∞[, a composition operator is said to be X,L_h-order bounded (we write (X,L_h)-ob) with $X = H^p$ or X = N if its composition with the map f ↦ f*, where f* denotes the radial limit of f, is order bounded from X into $L_h$. We give a complete characterization and a family of examples in both cases. On the other hand, we show that the ($N,log^{+}L$)-ob composition operators are exactly those which are Hilbert-Schmidt on $H^2$. We also prove that the ($N,L^q$)-ob composition operators are exactly those which are compact from N into $H^q$.
16
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.
17
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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 \(\mathbf{C}^n\).
18
Content available remote

Cesàro summability of one- and two-dimensional trigonometric-Fourier series

75%
Weisz F.
Colloquium Mathematicum
|
1997
|
tom 74
|
nr 1
123-133
EN
We introduce p-quasilocal operators and prove that if a sublinear operator T is p-quasilocal and bounded from $L_∞$ to $L_∞$ then it is also bounded from the classical Hardy space $H_p(T)$ to $L_p$ (0 < p ≤ 1). As an application it is shown that the maximal operator of the one-parameter Cesàro means of a distribution is bounded from $H_p(T)$ to $L_p$ (3/4 < p ≤ ∞) and is of weak type $(L_1,L_1)$. We define the two-dimensional dyadic hybrid Hardy space $H_{1}^{♯}(T^2)$ and verify that the maximal operator of the Cesàro means of a two-dimensional function is of weak type $(H_{1}^{♯}(T^2),L_1)$. So we deduce that the two-parameter Cesàro means of a function $f ∈ H_1^{♯}(T^2) ⊃ Llog L$ converge a.e. to the function in question.
19
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Content available

Holomorphic Sobolev spaces on the ball

66%
Beatrous F., Burbea J.
Instytut Matematyczny Polskiej Akademii Nauk
EN
CONTENTS Introduction ..............................................................5 0. Preliminaries and notation....................................6 1. Hilbert spaces of holomorphic functions..............11 2. Some estimates ..................................................16 3. The space $L^p_q$............................................22 4. Norm estimates...................................................30 5. Sobolev norms....................................................35 6. Projections in Sobolev spaces............................47 References.............................................................56
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