Weighted Inequalities for a Class of Volterra Convolution Operators

The purpose of this paper is to give necessary and sufficient conditions for the boundedness from L v p (R+) to L u q of Volterra convolution operators of the form k f ( x ) = ∫ 0 x k ( x − y ) f ( y ) d y , where k(x) is a non-negative non-decreasing kernel satisfying k(x+y)⩽D(k(x)+k(y)) for all x, yɛR+. The cases of 1 < p,q < ∞ and 0 < q < 1 < p < ∞ are considered. Also criteria for the compactness of K for 1 < p, q < ∞ are given.

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