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

Ildoo Kim; Kyeong Hun Kim; Sungbin Lim

doi:10.1016/j.jmaa.2015.12.040

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

Ildoo Kim, Kyeong Hun Kim, Sungbin Lim

Department of Mathematics

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

5 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 L_p-theory of high-order stochastic partial differential equations.

Original language	English
Pages (from-to)	1023-1047
Number of pages	25
Journal	Journal of Mathematical Analysis and Applications
Volume	436
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2015.12.040
Publication status	Published - 2016 Apr 15

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

Access to Document

10.1016/j.jmaa.2015.12.040

Cite this

Parabolic Littlewood-Paley inequality for a class of time-dependent pseudo-differential operators of arbitrary order, and applications to high-order stochastic PDE. / Kim, Ildoo ; Kim, Kyeong Hun; Lim, Sungbin.
In: Journal of Mathematical Analysis and Applications, Vol. 436, No. 2, 15.04.2016, p. 1023-1047.

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

@article{b2fea8bc40dd4e14b6724104f7a2f68c,

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

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",

author = "Ildoo Kim and Kim, {Kyeong Hun} and Sungbin Lim",

note = "Funding Information: This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education ( 2014R1A1A2055538 ). Publisher Copyright: {\textcopyright} 2015 Elsevier Inc.",

year = "2016",

month = apr,

day = "15",

doi = "10.1016/j.jmaa.2015.12.040",

language = "English",

volume = "436",

pages = "1023--1047",

journal = "Journal of Mathematical Analysis and Applications",

issn = "0022-247X",

publisher = "Academic Press Inc.",

number = "2",

}

TY - JOUR

T1 - Parabolic Littlewood-Paley inequality for a class of time-dependent pseudo-differential operators of arbitrary order, and applications to high-order stochastic PDE

AU - Kim, Ildoo

AU - Kim, Kyeong Hun

AU - Lim, Sungbin

N1 - Funding Information: This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education ( 2014R1A1A2055538 ). Publisher Copyright: © 2015 Elsevier Inc.

PY - 2016/4/15

Y1 - 2016/4/15

N2 - 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.

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.

KW - Non-local operators of arbitrary order

KW - Parabolic Littlewood-Paley inequality

KW - Stochastic partial differential equations

KW - Time-dependent high order operators

UR - http://www.scopus.com/inward/record.url?scp=84955187926&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2015.12.040

DO - 10.1016/j.jmaa.2015.12.040

M3 - Article

AN - SCOPUS:84955187926

SN - 0022-247X

VL - 436

SP - 1023

EP - 1047

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this