On the Operator ℒ(f) = f log |f|

Tadeusz Iwaniec, Anne Verde

Research output: Contribution to journalArticle

47 Scopus citations

Abstract

The present note deals with the operator ℒ: ℋ1(ℝn) → script D sign1(ℝn) which takes a given element f of the Hardy space to the function f log |f|. In general, this function need not be locally integrable. Nevertheless, due to peculiar cancellations of large positive and negative terms in the integral (Latin small letter esh) φ f log \f\ with φ ∈ C0 (ℝn), we are able to give meaning to f log |f| as a Schwartz distribution. We find several alternatives for this interpretation of f log |f|.

Original languageEnglish (US)
Pages (from-to)391-420
Number of pages30
JournalJournal of Functional Analysis
Volume169
Issue number2
DOIs
StatePublished - Dec 20 1999

Keywords

  • Distributions
  • Hardy space
  • Jacobians

ASJC Scopus subject areas

  • Analysis

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