On the boundedness of some potential‐type operators with oscillating kernels

Abstract

We consider a class of multidimensional potential-type operators with kernels that have singularities at the origin and on the unit sphere and that are oscillating at infinity. We describe some convex sets in the (1/p, 1/q)-plane for which these operators are bounded from Lp into Lq and indicate domains where they are not bounded. We also reveal some effects which show that oscillation and singularities of the kernels may strongly influence on the picture of boundedness of the operators under consideration.

Оценки Для Некоторых Операторов Свертки С Особенностями Ядер На Сферах

“…[4][5][6][7][8][9]). Случай особенностей ядер на нескольких сферах рассматривался ранее только в [6].…”