Parabolic martingales and non-symmetric Fourier multipliers

TL;DR

This paper introduces a new class of Fourier multipliers with non-symmetric symbols, providing explicit $L^p$ bounds using stochastic calculus and martingale inequalities.

Contribution

It develops a novel approach combining stochastic calculus of Lévy processes with martingale inequalities to analyze non-symmetric Fourier multipliers.

Findings

Established explicit $L^p$ bounds for new Fourier multipliers.

Extended Burkholder-Wang estimates to non-symmetric symbol context.

Provided a framework for analyzing non-symmetric Fourier multipliers.

Abstract

We give a class of Fourier multipliers with non-symmetric symbols and explicit norm bounds on $L^p$ spaces by using the stochastic calculus of L\'evy processes and Burkholder-Wang estimates for differentially subordinate martingales.