Multiplier extension and sampling theorem on Hardy spaces.

Sun Qiyu

Displaying similar documents to “Multiplier extension and sampling theorem on Hardy spaces.”

Spaces of sequences, sampling theorem, and functions of exponential type

Rodolfo Torres (1991)

Studia Mathematica

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We introduce certain spaces of sequences which can be used to characterize spaces of functions of exponential type. We present a generalized version of the sampling theorem and a "nonorthogonal wavelet decomposition" for the elements of these spaces of sequences. In particular, we obtain a discrete version of the so-called φ-transform studied in [6] [8]. We also show how these new spaces and the corresponding decompositions can be used to study multiplier operators on Besov spaces. ...

$L^{p}$ -multiplier theorems

W. Littman, C. McCarthy, N. Riviere (1968)

Studia Mathematica

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Variants of the Calderón-Zygmund theory for L-spaces.

Anthony Carbery (1986)

Revista Matemática Iberoamericana

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The purposes of this paper may be described as follows: (i) to provide a useful substitute for the Cotlar-Stein lemma for L^p-spaces (the orthogonality conditions are replaced by certain fairly weak smoothness asumptions); (ii) to investigate the gap between the Hörmander multiplier theorem and the Littman-McCarthy-Rivière example - just how little regularity is really needed? (iii) to simplify and extend the work of Duoandikoetxea...

A multiplier in Besov spaces which is not a multiplier in Lebesgue spaces

Hans Triebel (1979)

Banach Center Publications

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A class of Fourier multipliers on H¹(ℝ²)

Michał Wojciechowski (2000)

Studia Mathematica

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An integral criterion for being an $H^{1} (ℝ^{2})$ Fourier multiplier is proved. It is applied in particular to suitable regular functions which depend on the product of variables.

Note on Fourier series

L. S. Bosanquet, A. C. Offord (1935)

Compositio Mathematica

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Local Hardy spaces on Chébli-Trimèche hypergroups

Walter Bloom, Zengfu Xu (1999)

Studia Mathematica

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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.

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.

Transference theory onHardy and Sobolev spaces

Maria Carro, Javier Soria (1997)

Colloquium Mathematicae

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We show that the transference method of Coifman and Weiss can be extended to Hardy and Sobolev spaces. As an application we obtain the de Leeuw restriction theorems for multipliers.