Applications of Hörmander multiplier theorem to approximation in real Hardy spaces

1991 ◽  
pp. 119-129 ◽  
Author(s):  
Zhixin Liu ◽  
Shanzhen Lu
Keyword(s):  
Hardy Spaces ◽  
Multiplier Theorem

scholarly journals Convolution Operators and Bochner-Riesz Means on Herz-Type Hardy Spaces in the Dunkl Setting

2010 ◽  
Vol 2010 ◽  
pp. 1-17 ◽  
Author(s):  
A. Gasmi ◽  
F. Soltani
Keyword(s):  
Hardy Spaces ◽  
Multiplier Theorem ◽  
Convolution Operators ◽  
Riesz Means ◽  
Riesz Operators

We study the Dunkl convolution operators on Herz-type Hardy spacesℋα,2pand we establish a version of multiplier theorem for the maximal Bochner-Riesz operators on the Herz-type Hardy spacesℋα,∞p.

scholarly journals A Multiplier Theorem for Herz-Type Hardy Spaces Associated with the Dunkl Transform

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
A. Gasmi
Keyword(s):  
Hardy Spaces ◽  
Dunkl Transform ◽  
Multiplier Theorem

The main purpose of this paper is to establish a Hörmander multiplier theorem for Herz-type Hardy spaces associated with the Dunkl transform.

scholarly journals Spectral Multipliers of Self-Adjoint Operators on Besov and Triebel–Lizorkin Spaces Associated to Operators

2019 ◽  
Author(s):  
The Anh Bui ◽  
Xuan Thinh Duong
Keyword(s):  
Heat Kernel ◽  
Hardy Spaces ◽  
Adjoint Operator ◽  
Space Of Homogeneous Type ◽  
Multiplier Theorem ◽  
Homogeneous Type ◽  
Spectral Multipliers ◽  
Spectral Multiplier ◽  
Gaussian Estimate ◽  
Adjoint Operators

Abstract Let $X$ be a space of homogeneous type and let $L$ be a nonnegative self-adjoint operator on $L^2(X)$ that satisfies a Gaussian estimate on its heat kernel. In this paper we prove a Hörmander-type spectral multiplier theorem for $L$ on the Besov and Triebel–Lizorkin spaces associated to $L$. Our work not only recovers the boundedness of the spectral multipliers on $L^p$ spaces and Hardy spaces associated to $L$ but also is the 1st one that proves the boundedness of a general spectral multiplier theorem on Besov and Triebel–Lizorkin spaces.

Multiplier theorem for Hankel transform on Hardy spaces

2008 ◽  
Vol 159 (1-2) ◽  
pp. 1-12 ◽  
Author(s):  
Jacek Dziubański ◽  
Marcin Preisner
Keyword(s):  
Hardy Spaces ◽  
Hankel Transform ◽  
Multiplier Theorem

A multiplier theorem for one-sided Hardy spaces

2009 ◽  
Vol 139 (1) ◽  
pp. 209-223 ◽  
Author(s):  
C. Segovia ◽  
R. Testoni
Keyword(s):  
Hardy Spaces ◽  
Multiplier Theorem

In this paper we give a multiplier theorem for one-sided Hardy spaces which generalizes the results given by Strömberg and Torchinsky for two-sided weights. Also we state the $\smash{L_{\omega}^{p}}$ version with a Sawyer's weight ω.

scholarly journals Fourier Multipliers For Local Hardy Spaces On Chébli-Trimèche Hypergroups

1998 ◽  
Vol 50 (5) ◽  
pp. 897-928 ◽  
Author(s):  
Walter R. Bloom ◽  
Zengfu Xu
Keyword(s):  
Molecular Characterization ◽  
Hardy Spaces ◽  
Fourier Multipliers ◽  
Multiplier Theorem ◽  
Local Hardy Spaces

AbstractIn this paper we consider Fourier multipliers on local Hardy spaces hp (0 < p ≤ 1) for Chébli-Trimèche hypergroups. The molecular characterization is investigated which allows us to prove a version of Hörmander’s multiplier theorem.

scholarly journals Multipliers for Hardy spaces on locally compact Vilenkin groups

1993 ◽  
Vol 55 (3) ◽  
pp. 287-301 ◽  
Author(s):  
C. W. Onneweer ◽  
T. S. Quek
Keyword(s):  
Hardy Spaces ◽  
Vilenkin Group ◽  
Multiplier Theorem ◽  
Herz Spaces ◽  
Locally Compact ◽  
Vilenkin Groups

AbstractIn a recent paper In a recent paper the authors proved a multiplier theorem for Hardy spaces Hp (G), 0 < p ≤ 1, defined on a locally compact Vilenkin group G. The assumptions on the multiplier were expressed in terms of the “norms” of certain Herz spaces K (1/p − 1/?r, r, p) with r restricted to 1 ≤ r < ∞ and p < r. In the present paper we show how this restriction on r may be weakened to p ≤ r ∞. Furthermore, we present two modifications of our main theorem and compare these with certain results for multipliers on LP (Rn)-spaces, 1 < p < ∞, due to Seeger and to Cowling, Fendler and Foumier. We also discuss the sharpness of some of our results.

A Multiplier Theorem on Anisotropic Hardy Spaces

2018 ◽  
Vol 61 (2) ◽  
pp. 390-404 ◽  
Author(s):  
Li-an Daniel Wang
Keyword(s):  
Hardy Spaces ◽  
Multiplier Theorem ◽  
Multiplier Operator

AbstractWe present a multiplier theorem on anisotropic Hardy spaces. When m satisfies the anisotropic, pointwise Mihlin condition, we obtain boundedness of the multiplier operator Tm: → , for the range of p that depends on the eccentricities of the dilation A and the level of regularity of a multiplier symbol m. This extends the classical multiplier theorem of Taibleson andWeiss.

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