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 pro...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.展开更多
文摘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.