Approximation problems and representations of Hardy spaces in circular domains

I. Chalendar; J. Partington

Displaying similar documents to “Approximation problems and representations of Hardy spaces in circular domains”

Hardy type inequalities for two-parameter Vilenkin-Fourier coefficients

Péter Simon, Ferenc Weisz (1997)

Studia Mathematica

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Our main result is a Hardy type inequality with respect to the two-parameter Vilenkin system (*) $(\sum_{k = 1}^{\infty} \sum_{j = 1}^{\infty} {| f ̂ (k, j) |}^{p} {(k j)}^{p - 2})^{1 / p} \leq C_{p} ∥ f ∥_{H_{* *}^{p}}$ (1/2 < p≤2) where f belongs to the Hardy space $H_{* *}^{p} (G_{m} \times G_{s})$ 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.

Regularity of some nonlinear quantities on superharmonic functions in local Herz-type Hardy spaces.

Dashan Fan, Shanzhen Lu, Dachun Yang (1998)

Publicacions Matemàtiques

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In this paper, the authors introduce a kind of local Hardy spaces in R associated with the local Herz spaces. Then the authors investigate the regularity in these local Hardy spaces of some nonlinear quantities on superharmonic functions on R. The main results of the authors extend the corresponding results of Evans and Müller in a recent paper.

On reverse Hardy's inequality.

Alejandro García del Amo (1993)

Collectanea Mathematica

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Two-parameter Hardy-Littlewood inequalities

Ferenc Weisz (1996)

Studia Mathematica

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The inequality (*) $(\sum_{| n | = 1}^{\infty} \sum_{| m | = 1}^{\infty} {| n m |}^{p - 2} {| f ̂ (n, m) |}^{p})^{1 / p} \leq C_{p} ∥ ƒ ∥_{H_{p}}$ (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...

On the boundedness of multipliers, commutators and the second derivatives of Green’s operators on $H^{1}$ and $B M O$

Der-Chen Chang, Song-Ying Li (1999)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Intrinsic characterizations of distribution spaces on domains

V. Rychkov (1998)

Studia Mathematica

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We give characterizations of Besov and Triebel-Lizorkin spaces $B_{p q}^{s} (Ω)$ and $F_{p q}^{s} (Ω)$ in smooth domains $Ω \subset ℝ^{n}$ via convolutions with compactly supported smooth kernels satisfying some moment conditions. The results for s ∈ ℝ, 0 < p,q ≤ ∞ are stated in terms of the mixed norm of a certain maximal function of a distribution. For s ∈ ℝ, 1 ≤ p ≤ ∞, 0 < q ≤ ∞ characterizations without use of maximal functions are also obtained.

Some remarks on Triebel spaces

Jürgen Marschall (1987)

Studia Mathematica

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On Hardy spaces in complex ellipsoids

Thomas Hansson (1999)

Annales de l'institut Fourier

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This paper deals with atomic decomposition and factorization of functions in the holomorphic Hardy space $H^{1}$ . Such representation theorems have been proved for strictly pseudoconvex domains. The atomic decomposition has also been proved for convex domains of finite type. Here the Hardy space was defined with respect to the ordinary Euclidean surface measure on the boundary. But for domains of finite type, it is natural to define $H^{1}$ with respect to a certain measure that degenerates near...

$(H_{p}, L_{p})$ -type inequalities for the two-dimensional dyadic derivative

Ferenc Weisz (1996)

Studia Mathematica

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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 $f \in L_{1}$ is dyadically differentiable and its derivative is f a.e.