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

Stoica, Andrei LU (2017)
Abstract
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.
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author
supervisor
opponent
  • Professor Tuomas P. Hytönen, University of Helsinki, Finland
organization
publishing date
type
Thesis
publication status
published
subject
keywords
Calderón-Zygmund operator , martingale transform, Bellman function, dyadic Haar shift, UMD space, matrix A2 weight, weighted L2-space, Carleson embedding theorem
pages
122 pages
publisher
Lund University, Faculty of Science, Centre for Mathematical Sciences
defense location
Hörmander lecture hall, Sölvegatan 18A, Lund
defense date
2017-08-25 13:15
ISBN
978-91-7753-340-5
language
English
LU publication?
yes
id
74241ee2-fb21-4f53-8d1d-bb0058a37b75
date added to LUP
2017-05-30 11:52:53
date last changed
2017-08-10 13:41:55
@phdthesis{74241ee2-fb21-4f53-8d1d-bb0058a37b75,
  abstract     = {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.},
  author       = {Stoica, Andrei},
  isbn         = {978-91-7753-340-5},
  keyword      = {Calderón-Zygmund operator ,martingale transform,Bellman function,dyadic Haar shift,UMD space,matrix A2 weight,weighted L2-space,Carleson embedding theorem},
  language     = {eng},
  pages        = {122},
  publisher    = {Lund University, Faculty of Science, Centre for Mathematical Sciences},
  school       = {Lund University},
  title        = {Sharp Bounds for Calderón-Zygmund Operators in a Vector-Valued Setting},
  year         = {2017},
}