Intrinsic Square Function Characterizations of Hardy Spaces with Variable Exponents

Abstract

Let $p(\cdot ):{\mathbb{R}}^n\to (0,\infty )$ 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 $H^{p(\cdot )}({\mathbb{R}}^n)$ in terms of the Littlewood-Paley $g$-function, the Lusin area function and the $g_{\lambda }^{\ast }$-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 $g_{\lambda }^{\ast }$-function. The $p(\cdot )$-Carleson measure characterization for the dual space of $H^{p(\cdot )}({\mathbb{R}}^n)$, the variable exponent Campanato space ${\mathcal{L}}_{1,p(\cdot ),s}({\mathbb{R}}^n)$, in terms of the intrinsic function is also presented.

Bull. Malays. Math. Sci. Soc. (2) (to appear)

References in corpus (1)

• Weighted Endpoint Estimates for Multilinear Commutators of Marcinkiewicz Integrals