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Journal of the London Mathematical Society 1994 49(2):244-266; doi:10.1112/jlms/49.2.244
© 1994 by London Mathematical Society
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© The London Mathematical Society

Weighted Integral Inequalities for the Hardy Type Operator and the FractionalMaximal Operator

Lai Qinsheng

Department of Pure Mathematics, The University of Leeds Leeds, LS2 9JT

Received 19 March 1992. Revision received 9 June 1992.

Let w(x), u(x) and {upsilon}(x) be weight functions. In this paper, under appropriate conditions on Young's functions {Phi}1, {Phi}2 we characterize the inequality

Formula
for the Hardy-type operator T defined in [1] and the inequality

Formula
for the fractional maximal operator M{alpha}, {upsilon}; defined in [8], as well as the corresponding weak-type inequalities.


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