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Journal of the London Mathematical Society 1994 50(1):105-120; doi:10.1112/jlms/50.1.105
© 1994 by London Mathematical Society
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© The London Mathematical Society

Weighted Norm Inequalities of Hardy Type for a Class of Integral Operators

Vladimir D Stepanov

Khabarovsk State University Shelest 118-205, Khabarovsk 680042, Russian Federation E-mail: 1600{at}as.khabarovsk.su

Received 16 September 1992.

Necessary and sufficient conditions for the boundedness from Formula to Formula of Volterra integral operators of the form

Formula
where k(x,y) is a non-negative kernel under suitable monotone conditions, are given. The cases 1 <p ≤ q < {infty}, 1 < q < p < {infty} and 0 < q < l < p < {infty} are considered. The results extend the well-known weighted norm Hardy inequality.

The author's research was supported in part by SERC under Grant GR/H53419.


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