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MAXIMAL HARDY SPACES ASSOCIATED TO NONNEGATIVE SELF-ADJOINT OPERATORS

Part of: Harmonic analysis in several variables Parabolic equations and systems

Published online by Cambridge University Press:  23 December 2014

GUORONG HU
GUORONG HU*
Affiliation:
Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan email hugr@ms.u-tokyo.ac.jp
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Abstract

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Let $(X,d,{\it\mu})$ be a metric measure space satisfying the doubling, reverse doubling and noncollapsing conditions. Let $\mathscr{L}$ be a nonnegative self-adjoint operator on $L^{2}(X,d{\it\mu})$ satisfying a pointwise Gaussian upper bound estimate and Hölder continuity for its heat kernel. In this paper, we introduce the Hardy spaces $H_{\mathscr{L}}^{p}(X)$, $0<p\leq 1$, associated to $\mathscr{L}$ in terms of grand maximal functions and show that these spaces are equivalently characterised by radial and nontangential maximal functions.

Keywords

Hardy spacesmetric measure spacesself-adjoint operatorsGaussian heat kernel boundsmaximal functions

MSC classification

Primary: 42B30: $H^p$-spaces
Secondary: 42B35: Function spaces arising in harmonic analysis 35K08: Heat kernel
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 91 , Issue 2 , April 2015 , pp. 286 - 302
Copyright
Copyright © 2014 Australian Mathematical Publishing Association Inc. 

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