Weighted Hardy spaces associated to operators and boundedness of singular integrals

2012/02/09 by Bui, The Anh, Duong, Xuan Thinh
#35K05 #42B20 #42B25 #47B38 #58J35 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Secondary: 35B65

paper · doi:10.48550/arxiv.1202.2063

Abstract

Let (X, d, μ) be a space of homogeneous type, i.e. the measure μ satisfies doubling (volume) property with respect to the balls defined by the metric d. Let L be a non-negative self-adjoint operator on L²(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 ≤ 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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