Weighted Hardy spaces associated to operators and boundedness of singular integrals

The Anh Bui; Xuan Thinh Duong

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arXiv · 1202.2063

Weighted Hardy spaces associated to operators and boundedness of singular integrals

The Anh Bui·Xuan Thinh Duong

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Abstract

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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BibTeX RIS

The Anh Bui, Xuan Thinh Duong. 2012-02-09. Weighted Hardy spaces associated to operators and boundedness of singular integrals. https://arxiv.org/abs/1202.2063

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