Result: Multidimensional fractional integral operators and a general class of multivariable polynomials

The author presents a systematic study of some multidimensional fractional integral operators whose kernel involves a certain multivariable polynomial which was introduced earlier by the reviewer and \textit{M. Garg} [Rev. Roum. Phys. 32, 685-692 (1987; Zbl 0632.33005)]. Making use of the multidimensional Mellin transform and a special case of a multidimensional \(H\)-function transformation due to the reviewer and \textit{R. Panda} [Indagationes Math. 40, 118-131 (1978; Zbl 0392.44006)], she derives several interesting results (Theorems 1 to 4 in the paper) which are much too involved to be reproduced here. Finally, she considers a number of known or new corollaries of her main theorems.