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MAXIMAL HARDY SPACES ASSOCIATED TO NONNEGATIVE SELF-ADJOINT OPERATORS
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 91 / Issue 2 / April 2015
- Published online by Cambridge University Press:
- 23 December 2014, pp. 286-302
- Print publication:
- April 2015
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- Article
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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.
