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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 13:15:00
ISBN
978-91-7753-341-2
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
2022-04-11 12:35:15
@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         = {{978-91-7753-341-2}},
  keywords     = {{Calderón-Zygmund operator; martingale transform; Bellman function; dyadic Haar shift; UMD space; matrix A2 weight; weighted L2-space; Carleson embedding theorem}},
  language     = {{eng}},
  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}},
}