On Boundedness of a Certain Class of Hardy-Steklov Type Operators in Lebesgue Spaces (Report‪)‬

1. INTRODUCTION AND PRELIMINARIES Let 0 p [infinity], [[parallel] f[parallel] .sub.p] := [([[integral].sup.[infinity].sub.0] [[absolute value of f(x)].sup.p]dx).sup.1/p] and [L.sub.p] denote the Lebesgue space of all measurable functions on [R.sup.+] := [0, [infinity]) such that [[parallel] f[parallel] .sub.p] [infinity]. Here and throughout the paper the mark := is applied for introducing new notations and quantities. For the same purposes we make use of the mark =:.