Boundedness of Convolution Operators on Hardy Spaces

Establishing conditions for the boundedness of an operator taking H p ( R n ) into L p ( R n ) , with 0 < p ≤ 1 , is a classical subject. A standard approach to such problems is using the atomic characterization of H p ( R n ) , 0 < p ≤ 1 , and working with atoms. Unlike in certain earlier wor...

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Bibliographic Details
Published in:Computational methods and function theory Vol. 19; no. 2; pp. 183 - 191
Main Authors: Belinsky, Eduard, Liflyand, Elijah
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2019
Springer Nature B.V
Subjects:
Analysis
Atomic properties
Computational Mathematics and Numerical Analysis
Convolution
Functions of a Complex Variable
Mathematics
Mathematics and Statistics
Operators
Secondary 42B08
42B35
Primary 42B30
42B10
Fourier transform
42B15
Hardy space
Atomic decomposition
ISSN:1617-9447, 2195-3724
Online Access:Get full text
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Summary:Establishing conditions for the boundedness of an operator taking H p ( R n ) into L p ( R n ) , with 0 < p ≤ 1 , is a classical subject. A standard approach to such problems is using the atomic characterization of H p ( R n ) , 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.
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ISSN:1617-9447
2195-3724
DOI:10.1007/s40315-019-00269-w