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

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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 that this inequality gives a fundamental estimate for an Lp-theory of high-order stochastic partial differential equations.

Original languageEnglish
Pages (from-to)1023-1047
Number of pages25
JournalJournal of Mathematical Analysis and Applications
Volume436
Issue number2
DOIs
Publication statusPublished - 2016 Apr 15

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Keywords

  • Non-local operators of arbitrary order
  • Parabolic Littlewood-Paley inequality
  • Stochastic partial differential equations
  • Time-dependent high order operators

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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