Discrete Calderon's Identity, Atomic Decomposition and Boundedness Criterion of Operators on Multiparameter Hardy Spaces

作者：Han, Y.; Lu, G.^*; Zhao, K.

来源：Journal of Geometric Analysis, 2010, 20(3): 670-689.

DOI：10.1007/s12220-010-9123-6

• Boundedness
• Calderon-Zygmund operator
• Calderon's identity
• Multiparameter Hardy spaces
• Atomic decomposition
• Boundedness criterion of operators

In this paper we establish a discrete Calderon's identity which converges in both L(q)(R(n+m)) (1< q < infinity) and Hardy space H(p)(R(n) x R(m)) (0 < p <= 1). Based on this identity, we derive a new atomic decomposition into (p, q)-atoms (1 < q < infinity) on H(p)(R(n) x R(m)) for 0 < p <= 1. As an application, we prove that an operator T, which is bounded on L(q) (R(n+m)) for some 1 < q < 8, is bounded from H(p)(R(n) x R(m)) to L(p)(R(n+m)) if and only if T is bounded uniformly on all (p, q)-product atoms in L(p)(R(n+m)). The similar result from H(p)(R(n) x R(m)) to H(p)(R(n) x R(m)) is also obtained.

• 出版日期2010-7
• 单位青岛大学