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    Two weighted inequalities for B-fractional integrals
    (SPRINGER INTERNATIONAL PUBLISHING AG, 2016) Eroglu, Ahmet; Hajibayov, Mubariz G.; Serbetci, Ayhan
    In this paper we prove a two weighted inequality for Riesz potentials I-alpha,I-gamma f (B-fractional integrals) associated with the Laplace-Bessel differential operator Delta(B)= Sigma(n)(i=1) partial derivative(2)/partial derivative x(i)(2) + Sigma(k)(j=1) gamma(j)/x(j) partial derivative/partial derivative xj. This result is an analog of Heinig's result (Indiana Univ. Math. J. 33(4):573-582, 1984) for the B-fractional integral. Further, the Stein-Weiss inequality for B-fractional integrals is proved as an application of this result.