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Journal of the London Mathematical Society 1993 s2-48(3):465-487; doi:10.1112/jlms/s2-48.3.465
© 1993 by London Mathematical Society
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© Oxford University Press

Integral Operators on the Cone of Monotone Functions

Vladimir D. Stepanov

Department of Mathematics, Khabarovsk State University Shelest 118-205, Khabarovsk 680042, RussiaE-mail: VLADS{at}HPICNIT.KHABAROVSK.SU

Necessary and sufficient conditions for the boundedness of linear integral operators from Formula(R+) to Formula(R+) restricted to the cones of monotone functions are given. In addition a general approach to a number of classical operators is explicitly described. In particular, we determine when the Hardy-Littlewood maximal operator is bounded in the classical Lorentz space {Gamma}p(v) consisting of those measurable functions on Rn such that Formula


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