A note on fractional integral operators defined by weights and non-doubling measures

Authors

  • Oscar Blasco
  • Vicente Casanova
  • Joaquín Motos

DOI:

https://doi.org/10.7146/math.scand.a-15138

Abstract

Given a metric measure space (X,d,μ), a weight w defined on (0,) and a kernel kw(x,y) satisfying the standard fractional integral type estimates, we study the boundedness of the operators Kwf(x)=Xkw(x,y)f(y)dμ(y) and ˜Kwf(x)=X(kw(x,y)kw(x0,y))f(y)dμ(y) on Lebesgue spaces Lp(μ) and generalized Lipschitz spaces Lipϕ, respectively, for certain range of the parameters depending on the n-dimension of μ and some indices associated to the weight w.

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Published

2010-06-01

How to Cite

Blasco, O., Casanova, V., & Motos, J. (2010). A note on fractional integral operators defined by weights and non-doubling measures. MATHEMATICA SCANDINAVICA, 106(2), 283–300. https://doi.org/10.7146/math.scand.a-15138

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Section

Articles