Weighted Hardy spaces associated to operators and boundedness of singular integrals

Details Weighted Hardy spaces associated to operators and boundedness of singular integrals Weighted Hardy spaces associated to operators and boundedness of singular integrals

2012-02-09

arxiv.org/abs/1202.2063v1

Mathematics

Classical Analysis and ODEs

28 pages

Scientific paper

Let $(X, d, \mu)$ be a space of homogeneous type, i.e. the measure $\mu$ satisfies doubling (volume) property with respect to the balls defined by the metric $d$. Let $L$ be a non-negative self-adjoint operator on $L^2(X)$. Assume that the semigroup of $L$ satisfies the Davies-Gaffney estimates. In this paper, we study the weighted Hardy spaces $H^p_{L,w}(X)$, $0 < p \le 1$, associated to the operator $L$ on the space $X$. We establish the atomic and the molecular characterizations of elements in $H^p_{L,w}(X)$. As applications, we obtain the boundedness on $\HL$ for the generalized Riesz transforms associated to $L$ and for the spectral multipliers of $L$.

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