A trace inequality for generalized potentials in Lebesgue spaces with variable exponent

David E. Edmunds, Vakhtang Kokilashvili, Alexander Meskhi
2004 Journal of Function Spaces and Applications  
A trace inequality for the generalized Riesz potentialsIα(x)is established in spacesLp(x)defined on spaces of homogeneous type. The results are new even in the case of Euclidean spaces. As a corollary a criterion for a two-weighted inequality in classical Lebesgue spaces for potentialsIα(x)defined on fractal sets is derived.
doi:10.1155/2004/502312 fatcat:ul4qxzq5a5dhfot5y5egnkzzgy