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May/June 2013 Boundedness of singular integrals and their commutators with BMO functions on Hardy spaces
The Anh Bui, Xuan Thinh Duong
Adv. Differential Equations 18(5/6): 459-494 (May/June 2013).

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 $L^p$, $0 < p \le 1$, and for the commutator of $T$ and a BMO function to be weak-type bounded on Hardy space $H_L^1$. 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 Schr\"odinger operator on a 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 $L$.

Citation

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The Anh Bui. Xuan Thinh Duong. "Boundedness of singular integrals and their commutators with BMO functions on Hardy spaces." Adv. Differential Equations 18 (5/6) 459 - 494, May/June 2013.

Information

Published: May/June 2013
First available in Project Euclid: 14 March 2013

zbMATH: 1275.42019
MathSciNet: MR3086462

Subjects:
Primary: 35B65 , 35K05 , 42B20 , 42B25 , 47B38 , 58J35

Rights: Copyright © 2013 Khayyam Publishing, Inc.

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Vol.18 • No. 5/6 • May/June 2013
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