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arXiv · 2509.07559

Fractional Sobolev logarithmic inequalities

Vivek Sahu
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Abstract

We establish new Euclidean Sobolev logarithmic inequalities in the framework of fractional Sobolev spaces and their weighted version. Our approach relies on a interpolation inequality, which can be viewed as a fractional Caffarelli-Kohn-Nirenberg type inequality. We further relate the optimal constant in this interpolation inequality to a corresponding variational problem. These results extend classical Sobolev logarithmic inequalities to the nonlocal Euclidean framework and provide new tools for analysis in fractional Sobolev spaces.

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Vivek Sahu. 2025-09-09. Fractional Sobolev logarithmic inequalities. https://arxiv.org/abs/2509.07559

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