Acta mathematica scientia, Series B >
BOUNDEDNESS OF RIESZ POTENTIALS IN NONHOMOGENEOUS SPACES
Received date: 2005-12-26
Revised date: 2006-06-09
Online published: 2008-04-20
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
Hu Guoen , Meng Yan , Yang Dachun . BOUNDEDNESS OF RIESZ POTENTIALS IN NONHOMOGENEOUS SPACES[J]. Acta mathematica scientia, Series B, 2008 , 28(2) : 371 -382 . DOI: 10.1016/S0252-9602(08)60039-9
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