Acta mathematica scientia,Series B

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BOUNDEDNESS OF RIESZ POTENTIALS IN NONHOMOGENEOUS SPACES

Hu Guoen; Meng Yan; Yang Dachun   

  1. School of Mathematical Sciences, Beijing Normal University
    Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, China
  • Received:2005-12-26 Revised:2006-06-09 Online:2008-04-20 Published:2008-04-20
  • Contact: Yang Dachun

Abstract:

For a class of linear operators including Riesz potentials on Rd
with a non-negative Radon measure μ, which only satisfies some growth condition, the authors prove that their boundedness in Lebesgue spaces
is equivalent to their boundedness in the Hardy space or certain weak type endpoint estimates, respectively. As an application, the authors obtain several new end estimates.

Key words: Riesz potential, Lebesgue space, Hardy space, RBMO space, boundedness, non-doubling measure

CLC Number: 

  • 47B06
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