Weighted \(L^p\) inequalities for a class of integral operators including the classical index transforms (Q5940342)

The authors study the properties of some integral operators acting on weighted spaces \(L^p(I,w)\) where \(I\subset R\) be an interval and \(w=w(x)\) satisfies some conditions. Particular cases include the transforms of Kontorovich-Lebedev, Mehler-Fock and \(_2F_1\)-index transform by \textit{N. Hayek Calil}, \textit{E. R. Negrin} and \textit{B. J. González} [A class of index transforms associated with Olevskií's, ``Proceedings of the XIVth Spanish-Portuguese Conference on Mathematics'', Vols. I--III (Puerto de la Cruz, 1989), pp. 401-405, University La Laguna, La Laguna, Spain (1990) (In Spanish); Rev. Téc. Fac. Ing., Univ. Zulia 15, No. 3, 167-171 (1992; Zbl 0767.44004)] and by \textit{N. Hayek Calil} and \textit{B. J. González} [J. Inst. Math. Comput. Sci., Math. Ser. 6, No. 1, 21-24 (1993; Zbl 0808.44007)].NEWLINENEWLINENEWLINEThe boundedness of these operators is proved from the \(L^p(I,w)\) into \(L^q(I,w)\), \(1<p <\infty\), \(p+q=pq\) and from the \(L^1(I,w)\) to \(L^\infty(I,w)\).