Boundedness of singular integrals and their commutators with BMO functions on Hardy spaces

2011/10/08 by Bui, The Anh, Duong, Xuan Thinh
#35B65 Secondary: 35K05 #42B20 #42B25 #47B38 #58J35 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1110.1770

Abstract

In this paper, we establish sufficient conditions for a singular integral T to be bounded from certain Hardy spaces H^p_L to Lebesgue spaces L^p, 0< p ≤ 1, and for the commutator of T and a BMO function to be weak-type bounded on Hardy space H_L¹. We then show that our sufficient conditions are applicable to the following cases: (i) T is the Riesz transform or a square function associated with the Laplace-Beltrami operator on a doubling Riemannian manifold, (ii) T is the Riesz transform associated with the magnetic Schrödinger operator on an Euclidean space, and (iii) T = g(L) is a singular integral operator defined from the holomorphic functional calculus of an operator L or the spectral multiplier of a non-negative self adjoint operator L.

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