A note on fractional integral operators defined by weights and non-doubling measures - Blasco, Oscar; Casanova, Vicente; Motos, Joaquín (MATHEMATICA SCANDINAVICA, 2010)
Given a metric measure space (X,d,μ), a weight w defined on (0,∞) and a kernel k_w(x,y) satisfying the standard fractional integral type estimates, we study the boundedness of the operators K_w f(x)=_X k_w(x,y)f(y) dμ(y) and K_w f(x)=_X (k_w(x,y)-k_w(x_0,y))f(y) dμ(y) on Lebesgue spaces L^p(μ) and generalized Lipschitz spaces Lip_φ, respectively, for certain range of the parameters depending on the n-dimension of μ and some indices associated to the weight w.