A Boundedness Criterion via Atoms for Linear Operators in Hardy Spaces
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- Yang, D. & Zhou, Y. Constr Approx (2009) 29: 207. doi:10.1007/s00365-008-9015-1
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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 Hp(ℝn) to some quasi-Banach space ℬ if and only if T maps all (p,2,s)-atoms into uniformly bounded elements of ℬ.