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    POTENTIAL OPERATORS ON CARLESON CURVES IN MORREY SPACES
    (Ankara Univ, Fac Sci, 2018) Eroglu, Ahmet; Dadashova, Irada B.
    In this paper we study the potential operator I-alpha in the Morrey space L-p,L-lambda and the spaces BMO de.ned on Carleson curves Gamma. We prove that for 0 < alpha < 1, I-alpha is bounded from the Morrey space L-p,L-lambda( Gamma) to L-q,L-lambda(Gamma) on simple Carleson curves if (and only if in the infinite simple Carleson curve 1/p - 1/q = alpha/(1 - lambda), 1 < p < (1 - lambda)/alpha, and from the spaces L-1,L-lambda(Gamma) to WLq,lambda(Gamma) (and only if in the in.nite case) 1 - 1/q = alpha/1-lambda.