Weighted Hardy spaces associated to operators and boundedness of singular integrals

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 $H_{L,w}^p(X)$, $0<p\le 1$, associated to the operator $L$ on the space $X$. We establish the atomic and the molecular characterizations of elements in $H_{L,w}^p(X)$. As applications, we obtain the boundedness on $\HL$ for the generalized Riesz transforms associated to $L$ and for the spectral multipliers of $L$.

26 pages, some minor errors were corrected

References in corpus (2)

• Maximal inequalities and Riesz transform estimates on $L^p$ spaces for Schrödinger operators with nonnegative potentials
• Musielak-Orlicz Hardy Spaces Associated with Operators and Their Applications

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