, Volume 29, Issue 2, pp 207-218
Date: 05 Mar 2008

A Boundedness Criterion via Atoms for Linear Operators in Hardy Spaces

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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.

Communicated by Pencho Petrushev.