A matrix weighted bilinear Carleson lemma and maximal function

Maria Carmen Reguera, Sandra Pott, Stefanie Petermichl

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Abstract

We prove a bilinear Carleson embedding theorem with matrix weight and scalar measure. In the scalar case, this becomes exactly the well known weighted bilinear Carleson embedding theorem. Although only allowing scalar Carleson measures, it is to date the only extension to the bilinear setting of the recent Carleson embedding theorem by Culiuc and Treil that features a matrix Carleson measure and a matrix weight. It is well known that a Carleson embedding theorem implies a Doob’s maximal inequality and this holds true in the matrix weighted setting with an appropriately defined maximal operator. It is also known that a dimensional growth must occur in the Carleson embedding theorem with matrix Carleson measure, even with trivial weight. We give a definition of a maximal type function whose norm in the matrix weighted setting
does not grow with dimension.
Original languageEnglish
Pages (from-to)1163-1180
Number of pages18
JournalAnalysis and Mathematical Physics
Volume9
Issue number3
Early online date27 Jun 2019
DOIs
Publication statusPublished - 1 Sep 2019

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Mathematical Physics

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