Maximal function characterizations of Musielak-Orlicz-Hardy spaces associated to non-negative self-adjointoperators satisfying Gaussian estimates

Dachun Yang; Sibei Yang

doi:10.3934/cpaa.2016031

Article Contents

2016, Volume 15, Issue 6: 2135-2160. Doi: 10.3934/cpaa.2016031

This issue Previous Article Some properties of positive solutions for an integral system with the double weighted Riesz potentials Next Article Sign-changing solutions for fourth order elliptic equations with Kirchhoff-type

Maximal function characterizations of Musielak-Orlicz-Hardy spaces associated to non-negative self-adjoint operators satisfying Gaussian estimates

Dachun Yang^1, and
Sibei Yang^2,

1.
School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex systems, Ministry of Education, Beijing 100875
2.
School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000

Received: November 30, 2015

Revised: April 30, 2016

Published: October 2016

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Abstract

Let $L$ be a non-negative self-adjoint operator on $L^2(\mathbb{R}^n)$ whose heat kernels have the Gaussian upper bound estimates. Assume that the growth function $\varphi:\mathbb{R}^n\times[0,\infty) \to[0,\infty)$ satisfies that $\varphi(x,\cdot)$ is an Orlicz function and $\varphi(\cdot,t)\in {\mathbb A}_{\infty}(\mathbb{R}^n)$ (the class of uniformly Muckenhoupt weights). Let $H_{\varphi,L}(\mathbb{R}^n)$ be the Musielak-Orlicz-Hardy space introduced via the Lusin area function associated with the heat semigroup of $L$. In this article, the authors obtain several maximal function characterizations of the space $H_{\varphi,L}(\mathbb{R}^n)$, which, especially, answer an open question of L. Song and L. Yan under an additional mild assumption satisfied by Schrödinger operators on $\mathbb{R}^n$ with non-negative potentials belonging to the reverse Hölder class, and second-order divergence form elliptic operators on $\mathbb{R}^n$ with bounded measurable real coefficients.

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Mathematics Subject Classification: Primary: 42B25; Secondary: 42B35, 46E30.

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