A Sobolev Interpolation Inequality and a Gross-Sobolev Logarithmic Inequality

Abstract

A sharp integral inequality is proved and used to obtain a Sobolev interpolation inequality. Further, a new proof of a Gross-Sobolev logarithmic inequality is constructed on the basis of the Sobolev interpolation inequality.

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Acknowledgments

The author wishes to express gratitude to the referee for useful remarks.

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Correspondence to Sh. M. Nasibov.

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Russian Text © The Author(s), 2020, published in Matematicheskie Zametki, 2020, Vol. 107, No. 6, pp. 894–901.

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Nasibov, S.M. A Sobolev Interpolation Inequality and a Gross-Sobolev Logarithmic Inequality. Math Notes 107, 977–983 (2020). https://doi.org/10.1134/S0001434620050296

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Keywords

  • Sobolev interpolation inequality
  • Hausdorff-Young inequality
  • Gross-Sobolev logarithmic inequality