Vector-Valued Singular Integrals Revisited-with Random Dyadic Cubes

Tuomas P. Hytönen. "Vector-Valued Singular Integrals Revisited-with Random Dyadic Cubes." Bulletin of the Polish Academy of Sciences. Mathematics 60.3 (2012): 269-283. <http://eudml.org/doc/281286>.

@article{TuomasP2012,
abstract = {The vector-valued T(1) theorem due to Figiel, and a certain square function estimate of Bourgain for translations of functions with a limited frequency spectrum, are two cornerstones of harmonic analysis in UMD spaces. In this paper, a simplified approach to these results is presented, exploiting Nazarov, Treil and Volberg's method of random dyadic cubes, which allows one to circumvent the most subtle parts of the original arguments.},
author = {Tuomas P. Hytönen},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {Calderón-Zygmund operator; martingale transform; random dyadic cubes; UMD spaces; operators on a Haar basis},
language = {eng},
number = {3},
pages = {269-283},
title = {Vector-Valued Singular Integrals Revisited-with Random Dyadic Cubes},
url = {http://eudml.org/doc/281286},
volume = {60},
year = {2012},
}

TY - JOUR
AU - Tuomas P. Hytönen
TI - Vector-Valued Singular Integrals Revisited-with Random Dyadic Cubes
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2012
VL - 60
IS - 3
SP - 269
EP - 283
AB - The vector-valued T(1) theorem due to Figiel, and a certain square function estimate of Bourgain for translations of functions with a limited frequency spectrum, are two cornerstones of harmonic analysis in UMD spaces. In this paper, a simplified approach to these results is presented, exploiting Nazarov, Treil and Volberg's method of random dyadic cubes, which allows one to circumvent the most subtle parts of the original arguments.
LA - eng
KW - Calderón-Zygmund operator; martingale transform; random dyadic cubes; UMD spaces; operators on a Haar basis
UR - http://eudml.org/doc/281286
ER -