Boundedness and Compactness of Integral Operators on Spaces of Homogeneous Type and Applications, I

Boundedness and Compactness of Integral Operators on Spaces of Homogeneous Type and Applications, II

“…In this section we shall give several applications of the theorems we have proved in Section 3 of [KRL1] and in Section 1 of the present paper.…”

“…Next we shall consider applications of Theorems 3.1 of [KRL1] and Theorem 1.1 of the present paper to X the boundary of a strictly pseudoconvex domain in n , a pseudoconvex domain of finite type in 2 , or a convex domain of finite type in n . Let be a bounded domain in n with C 2 boundary ∂ .…”

“…We know that the "norm" on the BMO space defined in Section 2 of [KRL1] is actually only a semi-norm. In order to define a norm for BMO space, when X is compact, one adds the L 1 norm to it.…”

“…This paper is a continuation of [KRL1]. Here we apply the machinery developed in that first work to study commutators of integral operators and other advanced properties of operators that arise naturally in harmonic analysis.…”

“…In Section 2 we shall apply some of the theorems established in the previous sections and the theorems proved in [KRL1] to prove theorems for holomorphic Hardy spaces and for BMO and VMO spaces on some domains in n . The main results for this paper are Theorem 1.1 and Theorems 2.2 and 2.4.…”