A Boundedness Criterion via Atoms for Linear Operators in Hardy Spaces

• DOI: 10.1007/s00365-008-9015-1
• Publication Date: 2008-03-04T14:37:39Z
• Authors: Dachun Yang; Yuan Zhou
• Keywords: Linear operators; Operator (biology); Linear map; Continuous linear operator

Let p∈(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.