Sharp Bounds for Calderón-Zygmund Operators in a Vector-Valued Setting
(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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/74241ee2-fb21-4f53-8d1d-bb0058a37b75
- author
- Stoica, Andrei LU
- supervisor
-
- Sandra Pott LU
- opponent
-
- Professor Tuomas P. Hytönen, University of Helsinki, Finland
- organization
- publishing date
- 2017
- 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}}, }