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Equimeasurable rearrangements of functions satisfying the reverse Hölder or the reverse Jensen inequality

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Abstract

Equimeasurable rearrangements of functions \(f\) satisfying the reverse Hölder or the reverse Jensen inequality are studied. It is shown that the equimeasurable rearrangements belong to the same class as the function \(f\), and a sharp estimate of the rearrangement norms via the norm of the function \(f\) is obtained.

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Acknowledgments

The author is sincerely thankful to A. A. Korenovskii for his encouragement, fruitful discussions and valuable advises.

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  1. Odessa I. I. Mechnikov National University, Dvoryanskaya 2, 65026, Odessa, Ukraine

    Ruslan Shanin

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  1. Ruslan Shanin
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Correspondence to Ruslan Shanin.

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Communicated by Salvatore Rionero.

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Shanin, R. Equimeasurable rearrangements of functions satisfying the reverse Hölder or the reverse Jensen inequality. Ricerche mat. 64, 217–228 (2015). https://doi.org/10.1007/s11587-015-0229-9

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  • DOI: https://doi.org/10.1007/s11587-015-0229-9

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