Convolution operators on the weighted Herz-type Hardy spaces

Ming Yi Lee

doi:10.1016/j.jat.2005.11.007

Convolution operators on the weighted Herz-type Hardy spaces

Ming Yi Lee

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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Abstract

A molecular characterization of the weighted Herz-type Hardy spaces H K_q^n(1/p-1/q),p (w, w) and H K_q^n(1/p-1/q),p (w, w) is given, by which the boundedness of the Hilbert transform and the Riesz transforms are proved on these space for 0 < p ≤ 1. These results are obtained by first deriving that the convolution operator T f = k * f is bounded on the weighted Herz-type Hardy spaces.

Original language	English
Pages (from-to)	197-210
Number of pages	14
Journal	Journal of Approximation Theory
Volume	138
Issue number	2
DOIs	https://doi.org/10.1016/j.jat.2005.11.007
State	Published - Feb 2006

Keywords

Central atom
Molecular characterization
Weighted Herz-type Hardy space

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10.1016/j.jat.2005.11.007

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title = "Convolution operators on the weighted Herz-type Hardy spaces",

abstract = "A molecular characterization of the weighted Herz-type Hardy spaces H Kqn(1/p-1/q),p (w, w) and H Kqn(1/p-1/q),p (w, w) is given, by which the boundedness of the Hilbert transform and the Riesz transforms are proved on these space for 0 < p ≤ 1. These results are obtained by first deriving that the convolution operator T f = k * f is bounded on the weighted Herz-type Hardy spaces.",

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AB - A molecular characterization of the weighted Herz-type Hardy spaces H Kqn(1/p-1/q),p (w, w) and H Kqn(1/p-1/q),p (w, w) is given, by which the boundedness of the Hilbert transform and the Riesz transforms are proved on these space for 0 < p ≤ 1. These results are obtained by first deriving that the convolution operator T f = k * f is bounded on the weighted Herz-type Hardy spaces.

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Convolution operators on the weighted Herz-type Hardy spaces

Abstract

Keywords

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