A MAXIMAL FUNCTION CHARACTERIZATION FOR HARDY SPACES ASSOCIATED TO NONNEGATIVE SELF-ADJOINT OPERATORS SATISFYING GAUSSIAN ESTIMATES

By Liang Song, Lixin Yan. 2015

63 citations recorded by the source corpus.

Let $L$ be a nonnegative, self-adjoint operator satisfying Gaussian estimates on $L^2(\RR^n)$. In this article we give an atomic decomposition for the Hardy spaces $ H^p_{L,max}(\R)$ in terms of the nontangential maximal functions associated with the heat semigroup of $L$, and this leads eventually to characterizations of Hardy spaces associated to $L$, via atomic decomposition or the nontangential maximal functions. The proofs are based on a modification of technique due to A. Calder\'on \cite{C}.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6bd40c817db37e87114e9d4d85c927e873da97a9

Citations in the corpus

• Maximal function characterizations for new local Hardy-type spaces on spaces of homogeneous type (2016, unknown): “This was proved in full only recently in [38] (see also [39]).”