TRACE INEQUALITIES FOR FRACTIONAL INTEGRALS IN CENTRAL MORREY SPACES

We study the trace inequality for fractional integrals K-alpha in central Morrey spaces. In particular, we establish necessary condition and sufficient condition governing the inequality vertical bar vertical bar K(alpha)f vertical bar vertical bar(q,lambda 2)(La) (X,nu) <= C vertical bar vertical bar f vertical bar vertical bar (p,lambda 1)(La) (X,mu)(,) where (X, rho, mu) is a space of homogeneous type, a is a point in X and nu is another measure on X. As a corollary, we have necessary and sufficient conditions on power-type weights d nu (x) = d(a, x)(beta)d mu(x) for the trace inequality. The results are new even for the Euclidean spaces.