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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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 certain integral operators. II
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by H. P. Heinig PDF
Proc. Amer. Math. Soc. 95 (1985), 387-395 Request permission

Abstract:

Conditions on nonnegative weight functions $u(x)$ and $\upsilon (x)$ are given which ensure that an inequality of the form ${(\smallint {\left | {Tf(x)} \right |^q}u(x)\;dx)^{1/q}} \leqslant C{(\smallint {\left | {f(x)} \right |^p}\upsilon (x)\;dx)^{1/p}}$ holds for $1 \leqslant q < p < \infty$, where $T$ is an integral operator of the form $\int _{ - \infty }^x {K(x,y)f(y)dy}$ or $\int _x^\infty {K(y,x)f(y)\;dy}$ and $C$ a constant independent of $f$. Specifically a number of inequalities for well-known classical operators are obtained. Inequalities of the above form for $1 \leqslant p \leqslant q < \infty$ were obtained in [1].
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Additional Information
  • © Copyright 1985 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 95 (1985), 387-395
  • MSC: Primary 26D10; Secondary 42A50, 44A10, 47G05
  • DOI: https://doi.org/10.1090/S0002-9939-1985-0806076-3
  • MathSciNet review: 806076