Contents V.1, N.1, 2010

  • INEQUALITIES FORB-CONVOLUTION OPERATORS
    AKIF D. GADJIEV, MUBARIZ G. HAJIBAYOV (pp. 41-52)

    • Abstract.

    TheB-convolution operators generated by the generalized shift operators associ-ated with the Laplace-Bessel operator are considered and three inequalities are proved for theseoperators. The first two inequalities are O’Neil type inequalities and third inequality is a gen-eralization of the Young inequality for theB-convolution integrals. The last inequality is alsoan extension of the Hardy-Littlewood-Sobolev theorem for theB-fractional integrals.

    Keywords:

    Laplace-Bessel differential operator,B-convolution, O’Neil inequality, Young in-equality, Lorentz space,B-fractional integral.

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