Hardy Spaces and their Subspaces

Elijah Liflyand

doi:10.1007/978-3-030-81892-0_6

Hardy Spaces and their Subspaces

Elijah Liflyand

Department of Mathematics

Southern Federal University

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

Abstract

As we have previously stated on a number of occasions, if g is integrable, its Hilbert transform is not necessarily integrable. Moreover, it can be even not locally integrable. When the Hilbert transform is integrable, we say that g is in the (real) Hardy space H¹: = H¹(ℝ). There are a variety of its characterizations (or, equivalently, definitions). The one given by means of the Hilbert transform is both important and convenient.

Original language	English
Title of host publication	Pathways in Mathematics
Publisher	Birkhauser
Pages	101-129
Number of pages	29
DOIs	https://doi.org/10.1007/978-3-030-81892-0_6
State	Published - 2021

Publication series

Name	Pathways in Mathematics
ISSN (Print)	2367-3451
ISSN (Electronic)	2367-346X

Bibliographical note

Publisher Copyright:
© 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Access to Document

10.1007/978-3-030-81892-0_6

Cite this

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Hardy Spaces and their Subspaces

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