INEQUALITIES FORB-CONVOLUTION OPERATORSAKIF 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.