Bourgain's discretization theorem and uniform approximation by affine functions

Postgraduate Thesis uoadl:1692027 727 Read counter

Unit:
Κατεύθυνση Θεωρητικά Μαθηματικά
Library of the School of Science
Deposit date:
2017-06-28
Year:
2017
Author:
Boci Erion
Supervisors info:
Απόστολος Γιαννόπουλος , Καθηγητής, Τμήμα Μαθηματικών, ΕΚΠΑ
Δημήτριος Γατζούρας , Καθηγητής, Τμήμα Μαθηματικών, ΕΚΠΑ
Τηλέμαχος Χατζηαφράτης , Καθηγητής, Τμήμα Μαθηματικών, ΕΚΠΑ
Original Title:
Το θεώρημα διακριτοποίησης του Bourgain και ομοιόμορφη προσέγγιση με αφφινικές συναρτήσεις
Languages:
Greek
Translated title:
Bourgain's discretization theorem and uniform approximation by affine functions
Summary:
The present thesis consists of two parts.

The first part relates to Bourgain's discretization theorem. We start with Ribe's theorem, which is the impetus for finding metric characterizations of Banach spaces. Then we present Bourgain's discretization theorem, and we get through it a second proof of Ribe's theorem.

The second part of the thesis deals with the uniform approximation by affine functions property. We present a theorem of T. Hytönen and A. Naor.
Main subject category:
Science
Other subject categories:
Mathematics
Analysis
Keywords:
Analysis, Functional analysis, Harmonic analysis, Littlewood-Paley-Stein theory, Poisson semigroup, Heat semigroup, Ribe's theorem, Bourgain's discretization theorem, Uniform approximation by affine functions, (UAAP) property
Index:
No
Number of index pages:
0
Contains images:
No
Number of references:
29
Number of pages:
82
UAAP.pdf (941 KB) Open in new window