Parabolic Littlewood-Paley inequality for a class of time-dependent operators of arbitrary order, and applications to higher order stochastic PDE

TL;DR

This paper establishes a parabolic Littlewood-Paley inequality for time-dependent operators of arbitrary order, providing key estimates for the $L_p$-theory of stochastic partial differential equations, with broad applications.

Contribution

It introduces a novel parabolic Littlewood-Paley inequality for time-dependent operators of any order, advancing the analysis of stochastic PDEs.

Findings

Proves a new inequality for a class of time-dependent operators.

Provides fundamental $L_p$-estimates for stochastic PDEs.

Enhances analytical tools for higher order stochastic PDEs.

Abstract

In this paper we prove a parabolic version of the Littlewood-Paley inequality for a class of time-dependent local and non-local operators of arbitrary order, and as an application we show this inequality gives a fundamental estimate for the $L_p$-theory of the stochastic partial differential equations.