Weighted norm inequalities for pseudo-pseudodifferential operators defined by amplitudes

Nicholas Michalowski, David J. Rule, Wolfgang Staubach

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

We prove weighted norm inequalities for pseudodifferential operators with amplitudes which are only measurable in the spatial variables. The result is sharp, even for smooth amplitudes. Nevertheless, in the case when the amplitude contains the oscillatory factor ?{mapping}ei|?|1-?, the result can be substantially improved. We extend the Lp-boundedness of pseudo-pseudodifferential operators to certain weights. End-point results are obtained when the amplitude is either smooth or satisfies a homogeneity condition in the frequency variable. Our weighted norm inequalities also yield the boundedness of commutators of these pseudodifferential operators with functions of bounded mean oscillation. © 2010 Elsevier Inc.

Original languageEnglish
Pages (from-to)4183-4209
Number of pages27
JournalJournal of Functional Analysis
Volume258
Issue number12
DOIs
Publication statusPublished - Jun 2010

Keywords

  • BMO commutator
  • Pseudo-pseudodifferential operator
  • Pseudodifferential operator
  • Weighted norm inequality

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