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.

Keywords

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

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This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2014R1A1A2055538).