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

2015/03/09 by Ildoo Kim, Kim, Ildoo, Kyeong-Hun Kim +3
Mathematics · #26D10 #35G05 #42B25 #47G30 #60H15 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:26D10 #msc:35G05 #msc:42B25 #msc:47G30 #msc:60H15

paper · pdf · doi:10.48550/arxiv.1503.02369

arxiv created 2015/03/09 · arxiv updated 2015/03/10

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 this inequality gives a fundamental estimate for the L_p-theory of the stochastic partial differential equations.

Related

• Parabolic Littlewood-Paley inequality for ϕ(-Δ)-type operators and applications to Stochastic integro-differential equations
• A critical parabolic Sobolev embedding via Littlewood-Paley decomposition
• Optimal orders of the best constants in the Littlewood-Paley inequalities
• A generalization of the Littlewood-Paley inequality for the fractional Laplacian (-Δ)^α/2
• A Generalization of Littlewood-Paley Type Inequality for Evolution Systems Associated with Pseudo Differential Operators