A theorem on weak type estimates for Riesz transforms and martingale transforms

Varopoulos, Nicolas Th.. "A theorem on weak type estimates for Riesz transforms and martingale transforms." Annales de l'institut Fourier 31.1 (1981): 257-264. <http://eudml.org/doc/74486>.

@article{Varopoulos1981,
abstract = {The Riesz transforms of a positive singular measure $\nu \in M(\{\bf R\}^n)$ satisfy the weak type inequality\begin\{\}m\Big [ \sum ^n\_\{j=1\} |R\_j\nu |&gt; \lambda \Big ] \ge \{C\Vert \nu \Vert \over \lambda \},~ \lambda &gt;0\end\{\}where $m$ denotes Lebesgue measure and $C$ is a positive constant only depending on $m$.},
author = {Varopoulos, Nicolas Th.},
journal = {Annales de l'institut Fourier},
keywords = {Riesz transforms; martingale transforms},
language = {eng},
number = {1},
pages = {257-264},
publisher = {Association des Annales de l'Institut Fourier},
title = {A theorem on weak type estimates for Riesz transforms and martingale transforms},
url = {http://eudml.org/doc/74486},
volume = {31},
year = {1981},
}

TY - JOUR
AU - Varopoulos, Nicolas Th.
TI - A theorem on weak type estimates for Riesz transforms and martingale transforms
JO - Annales de l'institut Fourier
PY - 1981
PB - Association des Annales de l'Institut Fourier
VL - 31
IS - 1
SP - 257
EP - 264
AB - The Riesz transforms of a positive singular measure $\nu \in M({\bf R}^n)$ satisfy the weak type inequality\begin{}m\Big [ \sum ^n_{j=1} |R_j\nu |&gt; \lambda \Big ] \ge {C\Vert \nu \Vert \over \lambda },~ \lambda &gt;0\end{}where $m$ denotes Lebesgue measure and $C$ is a positive constant only depending on $m$.
LA - eng
KW - Riesz transforms; martingale transforms
UR - http://eudml.org/doc/74486
ER -