A Boundedness Criterion via Atoms for Linear Operators in Hardy Spaces

作者：Yang Dachun^*; Zhou Yuan

来源：Constructive Approximation, 2009, 29(2): 207-218.

DOI：10.1007/s00365-008-9015-1

• Linear operator
• Boundedness criterion
• Hardy space
• Atom
• Calderon reproducing formula
• Quasi-Banach space

Let p is an element of (0, 1] and s >= [n(1/p - 1)], where [n(1/p - 1)] denotes the maximal integer no more than n(1/p - 1). In this paper, the authors prove that a linear operator T extends to a bounded linear operator from the Hardy space H(p)(R(n)) to some quasi-Banach space B if and only if T maps all (p, 2, s)-atoms into uniformly bounded elements of B.

• 出版日期2009-4
• 单位北京师范大学