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Zbl 0946.26014
Drábek, P.; Heinig, H.P.; Kufner, A.
Weighted modular inequalities for monotone functions.
(English)
[J] J. Inequal. Appl. 1, No.2, 183-197 (1997). ISSN 1029-242X/e

Summary: Weight characterizations of weighted modular inequalities for operators on the cone of monotone functions are given in terms of composition operators on arbitrary nonnegative functions with changes in weights. The results extend to modular inequalities, those corresponding to weighted Lebesgue spaces given by {\it E. T. Sawyer} [Stud. Math. 96, No. 2, 145-158 (1990; Zbl 0705.42014)]. Application to Hardy and fractional integral operators on monotone functions are given.
MSC 2000:
*26D15 Inequalities for sums, series and integrals of real functions
42B25 Maximal functions
46E30 Spaces of measurable functions

Keywords: Riemann-Liouville operators; Young function; Orlicz spaces; norms; Hardy type inequalities; weighted modular inequalities; fractional integral operators

Citations: Zbl 0705.42014

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