A matrix weighted bilinear Carleson lemma and maximal function

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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.

Detaljer

Författare
Enheter & grupper
Externa organisationer
  • Julius Maximilian University of Würzburg
  • University of Birmingham
Forskningsområden

Ämnesklassifikation (UKÄ) – OBLIGATORISK

  • Matematisk analys
Originalspråkengelska
TidskriftAnalysis and Mathematical Physics
StatusE-pub ahead of print - 2019 jun 27
PublikationskategoriForskning
Peer review utfördJa