首页|Non-symmetric differentially subordinate martingales and sharp weak-type bounds for Fourier multipliers
Non-symmetric differentially subordinate martingales and sharp weak-type bounds for Fourier multipliers
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维普
Let p＞2 be a given exponent.In this paper,we prove,with the best constant,the weak-type(p,p)inequality||Tmf||Lp,∞(Rd)≤ Cp||f||Lp(Rd)for a large class of non-symmetric Fourier multipliers Tm 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.
万方数据
维普
