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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Weighted norm inequalities for operators of Hardy type
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by Steven Bloom and Ron Kerman PDF
Proc. Amer. Math. Soc. 113 (1991), 135-141 Request permission

Abstract:

A new proof, yielding new conditions, is given for the two-weighted norm Hardy inequality. The theorem is extended to operators with kernels behaving much like the Riemann-Liouville fractional integrals of nonnegative order.
References
    G. Hardy, J. Littlewood, and G. Polya, Inequalities, Cambridge Univ. Press, 1967. F. Martin-Reyes and E. Sawyer, Weighted norm inequalities for the Riemann-Liouville fractional integral operators, preprint.
  • V. D. Stepanov, Two-weight estimates for Riemann-Liouville integrals, Izv. Akad. Nauk SSSR Ser. Mat. 54 (1990), no. 3, 645–656 (Russian); English transl., Math. USSR-Izv. 36 (1991), no. 3, 669–681. MR 1072699, DOI 10.1070/IM1991v036n03ABEH002039
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Additional Information
  • © Copyright 1991 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 113 (1991), 135-141
  • MSC: Primary 26D15; Secondary 26A33
  • DOI: https://doi.org/10.1090/S0002-9939-1991-1059623-6
  • MathSciNet review: 1059623