摘要
The main purpose of this paper is to derive a new （p,q）-atomic decomposition on the multi-parameter Hardy space HP（X1 × X2） for 0 〈 po 〈 P ≤ 1 for some po and all 1 〈 q 〈 ∞, where X1 ×X2 is the product of two spaces of homogeneous type in the sense of Coifman and Weiss. This decomposition converges in both L^q（X1 × X2） （for 1 〈 q 〈 ∞） and Hardy space HP（X1× X2） （for 0 〈 p _〈 1）. As an application, we prove that an operator T, which is bounded on Lq（X1× X2） for some 1 〈 q 〈 ∞, is bounded from H^p（X1 × X2） to L^p（X1 × X2） if and only if T is bounded uniformly on all （p, q）-product atoms in LP（X1 × X2）. The similar boundedness criterion from HP（X1 × X2） to HP（X1 × X2） is also obtained.
The main purpose of this paper is to derive a new （p,q）-atomic decomposition on the multi-parameter Hardy space HP（X1 × X2） for 0 〈 po 〈 P ≤ 1 for some po and all 1 〈 q 〈 ∞, where X1 ×X2 is the product of two spaces of homogeneous type in the sense of Coifman and Weiss. This decomposition converges in both L^q（X1 × X2） （for 1 〈 q 〈 ∞） and Hardy space HP（X1× X2） （for 0 〈 p _〈 1）. As an application, we prove that an operator T, which is bounded on Lq（X1× X2） for some 1 〈 q 〈 ∞, is bounded from H^p（X1 × X2） to L^p（X1 × X2） if and only if T is bounded uniformly on all （p, q）-product atoms in LP（X1 × X2）. The similar boundedness criterion from HP（X1 × X2） to HP（X1 × X2） is also obtained.
基金
Supported by U.S. NSF (Grant No. DMS#0901761)
