Mathematics – Classical Analysis and ODEs
Scientific paper
2011-10-08
Mathematics
Classical Analysis and ODEs
36 pages
Scientific paper
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 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 $L$.
Bui The Anh
Duong Xuan Thinh
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