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Sharp Bounds for Calderón-Zygmund Operators in a Vector-Valued Setting

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Author

  • Andrei Stoica

Summary, in English

In this thesis we extend several classical results about Calderón-Zygmund operators to spaces of vector-valued functions. We first obtain bounds for the norm of dyadic Haar shift operators using a Bellman function technique, and then apply the representation theorem to obtain corresponding results for general Calderón-Zygmund operators. We discuss several results for UMD space-valued Calderón-Zygmund operators and show some weighted inequalities for matrix-valued weights. We also prove a version of the matrix-weighted Carleson embedding theorem.

Publishing year

2017

Language

English

Document type

Dissertation

Publisher

Lund University, Faculty of Science, Centre for Mathematical Sciences

Topic

  • Mathematical Analysis

Keywords

  • Calderón-Zygmund operator
  • martingale transform
  • Bellman function
  • dyadic Haar shift
  • UMD space
  • matrix A2 weight
  • weighted L2-space
  • Carleson embedding theorem

Status

Published

Supervisor

ISBN/ISSN/Other

  • ISBN: 978-91-7753-341-2
  • ISBN: 978-91-7753-340-5

Defence date

25 August 2017

Defence time

13:15

Defence place

Hörmander lecture hall, Sölvegatan 18A, Lund

Opponent

  • Tuomas P. Hytönen (Professor)