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 language | English |
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Title of host publication | Applied and Numerical Harmonic Analysis |
Publisher | Springer International Publishing |
Pages | 85-98 |
Number of pages | 14 |
DOIs | |
State | Published - 2019 |
Publication series
Name | Applied and Numerical Harmonic Analysis |
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ISSN (Print) | 2296-5009 |
ISSN (Electronic) | 2296-5017 |
Bibliographical note
Publisher Copyright:© 2019, Springer Nature Switzerland AG.