A trace inequality for generalized potentials in Lebesgue spaces with variable exponent
David E. Edmunds,1Vakhtang Kokilashvili,2and Alexander Meskhi2
Academic Editor: Vladimir Stepanov
Received01 May 2003
Abstract
A trace inequality for the generalized Riesz potentials Iα(x) is established in spaces Lp(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 potentials Iα(x) defined on fractal sets is derived.