A Multidimensional Hardy–Littlewood Theorem

Elijah Liflyand; Ulrich Stadtmüller

doi:10.1007/978-3-030-12277-5_14

A Multidimensional Hardy–Littlewood Theorem

Elijah Liflyand, Ulrich Stadtmüller

Department of Mathematics

Ulm University

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

Two classical results by F. and M. Riesz on absolute continuity and by Hardy and Littlewood on the absolutely convergence of Fourier series for a function f with bounded variation, whose conjugate is also of bounded variation, are generalized. We improve earlier obtained one-dimensional non-periodic versions and present multidimensional extensions for Hardy’s variation.

Original language	English
Title of host publication	Applied and Numerical Harmonic Analysis
Publisher	Springer International Publishing
Pages	227-240
Number of pages	14
DOIs	https://doi.org/10.1007/978-3-030-12277-5_14
State	Published - 2019

Publication series

Name	Applied and Numerical Harmonic Analysis
ISSN (Print)	2296-5009
ISSN (Electronic)	2296-5017

Bibliographical note

Publisher Copyright:
© 2019, Springer Nature Switzerland AG.

Keywords

Absolute continuity
Bounded variation
Brothers Riesz theorem
Fourier transform
Hardy space
Hardy–Littlewood theorem
Hardy’s variation
Hilbert transform

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10.1007/978-3-030-12277-5_14

Cite this

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KW - Hardy space

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KW - Hilbert transform

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A Multidimensional Hardy–Littlewood Theorem

Abstract

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Keywords

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