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

Ildoo Kim; Kyeong Hun Kim; Panki Kim

doi:10.1016/j.aim.2013.09.008

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

Ildoo Kim, Kyeong Hun Kim, Panki Kim

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

22 Citations (Scopus)

Abstract

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 + gd_{W t}.

Original language	English
Pages (from-to)	161-203
Number of pages	43
Journal	Advances in Mathematics
Volume	249
DOIs	https://doi.org/10.1016/j.aim.2013.09.008
Publication status	Published - 2013 Dec 20

Keywords

Estimates of transition functions
Integro-differential operators
Lévy processes
Parabolic Littlewood-Paley inequality
Stochastic partial differential equations

ASJC Scopus subject areas

General Mathematics

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10.1016/j.aim.2013.09.008

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

abstract = "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.",

keywords = "Estimates of transition functions, Integro-differential operators, L{\'e}vy processes, Parabolic Littlewood-Paley inequality, Stochastic partial differential equations",

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AU - Kim, Ildoo

AU - Kim, Kyeong Hun

AU - Kim, Panki

PY - 2013/12/20

Y1 - 2013/12/20

N2 - 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.

AB - 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.

KW - Estimates of transition functions

KW - Integro-differential operators

KW - Lévy processes

KW - Parabolic Littlewood-Paley inequality

KW - Stochastic partial differential equations

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DO - 10.1016/j.aim.2013.09.008

M3 - Article

AN - SCOPUS:84884972376

SN - 0001-8708

VL - 249

SP - 161

EP - 203

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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