Non-symmetric differentially subordinate martingales and sharp weak-type bounds for Fourier multipliers  

作　　者：Meryem Akboudj Yong Jiao Adam Osękowski 

机构地区：[1]School of Mathematics and Statistics,Hunan Key Laboratory of Analytical Mathematics and Applications,Central South University,Changsha 410075,China [2]Faculty of Mathematics,Informatics and Mechanics,University of Warsaw,Warsaw 02-097,Poland

出　　处：《Science China Mathematics》2024年第8期1807-1826,共20页中国科学（数学）（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.12125109 and 11961131003)。

摘　　要：Let p>2 be a given exponent.In this paper,we prove,with the best constant,the weak-type(p,p)inequality■for a large class of non-symmetric Fourier multipliers T_(m) obtained via modulation of jumps of certain Lévy processes.In particular,the estimate holds for appropriate linear combinations of second-order Riesz transforms and skew versions of the Beurling-Ahlfors operator on the complex plane.The proof rests on a novel probabilistic bound for Hilbert-space-valued martingales satisfying a certain non-symmetric subordination principle.Further applications to harmonic functions and Riesz systems on Euclidean domains are indicated.

关 键 词：weak-type bound Fourier multiplier MARTINGALE differential subordination laminate 

分 类 号：O177[理学—数学]