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Boundedness of Convolution Operators on Hardy Spaces

Boundedness of Convolution Operators on Hardy Spaces Establishing conditions for the boundedness of an operator taking $$H^p({\mathbb {R}}^n)$$ H p ( R n ) into $$L^p({\mathbb {R}}^n)$$ L p ( R n ) , with $$0<p\le 1$$ 0 < p ≤ 1 , is a classical subject. A standard approach to such problems is using the atomic characterization of $$H^p({\mathbb {R}}^n)$$ H p ( R n ) , $$0<p\le 1$$ 0 < p ≤ 1 , and working with atoms. Unlike in certain earlier work on the subject we apply this machinery not to specific operators but to a wide general family of multivariate linear means generated by a multiplier. We illustrate the use of these new conditions applying them to some methods known from before. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

Boundedness of Convolution Operators on Hardy Spaces

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Publisher
Springer Journals
Copyright
Copyright © 2019 by Springer-Verlag GmbH Germany, part of Springer Nature
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/s40315-019-00269-w
Publisher site
See Article on Publisher Site

Abstract

Establishing conditions for the boundedness of an operator taking $$H^p({\mathbb {R}}^n)$$ H p ( R n ) into $$L^p({\mathbb {R}}^n)$$ L p ( R n ) , with $$0<p\le 1$$ 0 < p ≤ 1 , is a classical subject. A standard approach to such problems is using the atomic characterization of $$H^p({\mathbb {R}}^n)$$ H p ( R n ) , $$0<p\le 1$$ 0 < p ≤ 1 , and working with atoms. Unlike in certain earlier work on the subject we apply this machinery not to specific operators but to a wide general family of multivariate linear means generated by a multiplier. We illustrate the use of these new conditions applying them to some methods known from before.

Journal

Computational Methods and Function TheorySpringer Journals

Published: Apr 29, 2019

References