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Boundedness of fractional integrals in Hardy spaces with non-doubling measure

— In memory of professor Sun Yongsheng

  • Published:
Analysis in Theory and Applications

Abstract

Let μ be a Borel measure on ℝd which may be non doubling. The only condition that μ must satisfy is μ(Q)≤c0l(Q)n for any cubeQ ⊂ ℝd with sides parallel to the coordinate axes and for some fixed n with 0 < n ≤d. The purpose of this paper is to obtain a boundedness property of fractional integrals in Hardy spaces H1(μ).

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Authors and Affiliations

  1. Institute of Applied Physics and Computational Mathematics, P. O. Box 8009, 100088, Beijing, P.C. China

    Wengu G. Chen

  2. Department of Mathematics, 266071, Quingdo, College of Teachers Qingdao University, P. C. China

    Yixin X. Lai

Authors
  1. Wengu G. Chen
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  2. Yixin X. Lai
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Additional information

The first author was supported by NNSF of China (No.10371080) and Scientific Research Foundation for Returned Overseas Chinese Scholars.

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Chen, W.G., Lai, Y.X. Boundedness of fractional integrals in Hardy spaces with non-doubling measure. Analysis in Theory and Applications 22, 195–200 (2006). https://doi.org/10.1007/BF03218712

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  • DOI: https://doi.org/10.1007/BF03218712

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