Abstract
In this article, we study the connection between the fractional Moser—Trudinger inequality and the fractional (\({{kp} \over {p - 1}}\), p)-Poincaré type inequality for any Euclidean domain and discuss the sharpness of this inequality whose analogous results are well known in the local case. We further provide sufficient conditions on domains for fractional (q, p)-Porncaré type inequalities to hold. We also derive Adachi—Tanaka type inequalities in the non-local setting.
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Acknowledgements
The author would like to thank his advisor Professor Prosenjit Roy for his encouragement on the subject. The author would also like to thank Prof. Gyula Csató for fruitful discussions and comments on this research.
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Sk, F. Remarks on the Fractional Moser—Trudinger Inequality. JAMA 148, 447–470 (2022). https://doi.org/10.1007/s11854-022-0234-3
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DOI: https://doi.org/10.1007/s11854-022-0234-3