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On Boundedness of Weighted Hardy Operator in and Regularity Condition

Abstract

We give a new proof for power-type weighted Hardy inequality in the norms of generalized Lebesgue spaces . Assuming the logarithmic conditions of regularity in a neighborhood of zero and at infinity for the exponents , necessary and sufficient conditions are proved for the boundedness of the Hardy operator from into . Also a separate statement on the exactness of logarithmic conditions at zero and at infinity is given. This shows that logarithmic regularity conditions for the functions at the origin and infinity are essentially one.

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Correspondence to FarmanImran Mamedov.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Harman, A., Mamedov, F. On Boundedness of Weighted Hardy Operator in and Regularity Condition. J Inequal Appl 2010, 837951 (2010). https://doi.org/10.1155/2010/837951

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  • DOI: https://doi.org/10.1155/2010/837951

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