Littlewood-Paley Characterization for Musielak-Orlicz-Hardy Spaces Associated with Operators

2019/03/20 by Shen, Jiawei, Chen, Zhitian, Long, Shunchao
#42B20 #42B25 #42B30 #42B35 #46E30 #47B38 #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1903.08393

Abstract

Let X be a space of homogeneous type. Assume that L is an non-negative second-order self-adjoint operator on L²(X) with (heart) kernel associated to the semigroup e ^{- tL} that satisfies the Gaussian upper bound. In this paper, the authors introduce a new characterization of the Musielak-Orlicz-Hardy Space H_{φ, L}(X) associated with L in terms of the Lusin area function where φ is a growth function. Further, the authors prove that the Musielak-Orlicz-Hardy Space H_L,G,φ(X) associated with L in terms of the Littlewood-Paley function is coincide with H_{φ, L}(X) and their norms are equivalent.

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