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.
Bibliographical noteFunding 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 ).
© 2015 Elsevier Inc.
- Non-local operators of arbitrary order
- Parabolic Littlewood-Paley inequality
- Stochastic partial differential equations
- Time-dependent high order operators
ASJC Scopus subject areas
- Applied Mathematics