Parabolic Littlewood-Paley inequality for φ(- δ)-type operators and applications to stochastic integro-differential equations

摘要

In this paper we prove a parabolic version of the Littlewood-Paley inequality (1.4) for the operators of the type φ(- δ), where φ is a Bernstein function. As an application, we construct an L p-theory for the stochastic integro-differential equations of the type d u = (- φ(- δ)u + f)d t + gdW t.