Hardy Spaces and their Subspaces

Elijah Liflyand

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


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 languageEnglish
Title of host publicationPathways in Mathematics
Number of pages29
StatePublished - 2021

Publication series

NamePathways 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.


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