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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3 Citations (Scopus)

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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Stochastic PDEs
Pseudodifferential Operators
Partial differential equations
Higher Order
Stochastic Partial Differential Equations
Arbitrary
Operator
Estimate
Class

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

Cite this

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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.",
keywords = "Non-local operators of arbitrary order, Parabolic Littlewood-Paley inequality, Stochastic partial differential equations, Time-dependent high order operators",
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AU - Kim, Kyeong Hun

AU - Lim, Sungbin

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AB - 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.

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KW - Stochastic partial differential equations

KW - Time-dependent high order operators

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