A Generalization of Littlewood-Paley Type Inequality for Evolution Systems Associated with Pseudo Differential Operators

2025/02/21 by Ji, Un Cig, Kim, Jae Hun
#42B25 #42B37 #47G30 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2502.15221

Abstract

In this paper, we first prove that the Littlewood-Paley g-function, related to the convolution corresponding to the composition of pseudo-differential operator and evolution system associated with pseudo-differential operators, is a bounded operator from L^q((a,b)× ℝ^d;V) with a Hilbert space V into L^q((a,b)× ℝ^d). Secondly, we prove that the sharp function of the Littlewood-Paley g-function is bounded by some maximal function. Finally, by applying Fefferman-Stein theorem and Hardy-Littlewood maximal theorem, we prove the Littlewood-Paley type inequality for evolution systems associated with pseudo-differential operators.

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