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Journal of the London Mathematical Society 1992 s2-45(2):232-242; doi:10.1112/jlms/s2-45.2.232
© 1992 by London Mathematical Society
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© Oxford University Press

Weighted Inequalities for a Class of Volterra Convolution Operators

Vladimir D. Stepanov

Mathematics Department, University of Alabama Box 870350, Tuscaloosa, Alabama 35487-0350, USA

The purpose of this paper is to give necessary and sufficient conditions for the boundedness from Formula(R+) to Formula of Volterra convolution operators of the form Formula, where k(x) is a non-negative non-decreasing kernel satisfying k(x+y)≤D(k(x)+k(y)) for all x, y{varepsilon}R+. The cases of 1 < p,q < {infty} and 0 < q < 1 < p < {infty} are considered. Also criteria for the compactness of K for 1 < p, q < {infty} are given.

Current address: Institute for Applied Mathematics, Frunze 72, Khabarovsk 680002, Russian Federation


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