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

Autores: Óscar Blasco de la Cruz , Vicente Casanova, Joaquín Motos Izquierdo
Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 106, Nº 2, 2010, págs. 283-300
Idioma: inglés
DOI: 10.7146/math.scand.a-15138
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Resumen
- 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 K~wf(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.