Integrability spaces: wide, wider and widest

Elijah Liflyand

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

Abstract

In this chapter, we discuss how wide a space for the integrability of the Fourier transform of a function of bounded variation can be. Of course, we continue to make use of the natural assumption of local absolute continuity. Also, our functions vanish at infinity. What is naturally related to this is, on the one hand, a very general asymptotic formula for the sine Fourier transform, and, on the other hand, a variety of subspaces of the class of functions of bounded variation each of them has its own “integrability position”. It will be shown that all these are connected to various versions and refinements of the Fourier-Hardy inequality (1.61). This chapter mainly refers to the recent publications [118] and [121].

Original languageEnglish
Title of host publicationApplied and Numerical Harmonic Analysis
PublisherSpringer International Publishing
Pages85-98
Number of pages14
DOIs
StatePublished - 2019

Publication series

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

Bibliographical note

Publisher Copyright:
© 2019, Springer Nature Switzerland AG.

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