Global Stein theorem on Hardy spaces

A. Bonami, S. Grellier, B. F. Sehba

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

Let f be an integrable function which has integral 0 on Rn.What is the largest condition on |f| that guarantees that f is in the Hardy spaceH1(Rn)? When f is compactly supported, it is well-known that the largest conditionon |f| is the fact that |f|∈LlogL(Rn). We consider the same kind ofproblem here, but without any condition on the support. We do so for H1(Rn),as well as for the Hardy space Hlog(Rn) which appears in the study of pointwiseproducts of functions in H1(Rn) and in its dual BMO.

Original languageEnglish
JournalAnalysis Mathematica
DOIs
Publication statusAccepted/In press - 2024

Keywords

  • 42B25
  • 42B30
  • 46E30
  • Hardy space
  • Hardy-Musielak space
  • Stein theorem

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