Constructive Approximation

, Volume 29, Issue 2, pp 207–218

A Boundedness Criterion via Atoms for Linear Operators in Hardy Spaces

Article

DOI: 10.1007/s00365-008-9015-1

Cite this article as:
Yang, D. & Zhou, Y. Constr Approx (2009) 29: 207. doi:10.1007/s00365-008-9015-1

Abstract

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.

Keywords

Linear operatorBoundedness criterionHardy spaceAtomCalderón reproducing formulaQuasi-Banach space

Mathematics Subject Classification (2000)

42B2042B3042B25

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, Ministry of EducationBeijing Normal UniversityBeijingPeople’s Republic of China