Intrinsic Square Function Characterizations of Hardy Spaces with Variable Exponents

2014/11/20 by Zhuo, Ciqiang, Yang, Dachun, Liang, Yiyu
#42B35 #46E30 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Primary: 42B25 #Secondary: 42B30

paper · doi:10.48550/arxiv.1411.5535

Abstract

Let p(⋅): \mathbb Rⁿ→(0,∞) be a measurable function satisfying some decay condition and some locally log-Hölder continuity. In this article, via first establishing characterizations of the variable exponent Hardy space H^p(⋅)(\mathbb Rⁿ) in terms of the Littlewood-Paley g-function, the Lusin area function and the g_λ^∗-function, the authors then obtain its intrinsic square function characterizations including the intrinsic Littlewood-Paley g-function, the intrinsic Lusin area function and the intrinsic g_λ^∗-function. The p(⋅)-Carleson measure characterization for the dual space of H^p(⋅)(\mathbb Rⁿ), the variable exponent Campanato space L_1,p(⋅),s(\mathbb Rⁿ), in terms of the intrinsic function is also presented.

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