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leray–trudinger inequality

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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Series expansion of Leray–Trudinger inequality
Part of
Xiaomei Sun, Kaixiang Yu, Anqiang Zhu
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 153 / Issue 1 / February 2023

Published online by Cambridge University Press:

20 December 2021, pp. 262-274

Print publication:

February 2023
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In this paper, we establish an infinite series expansion of Leray–Trudinger inequality, which is closely related with Hardy inequality and Moser Trudinger inequality. Our result extends early results obtained by Mallick and Tintarev [A. Mallick and C. Tintarev. An improved Leray-Trudinger inequality. Commun. Contemp. Math. 20 (2018), 17501034. OP 21] to the case with many logs. It should be pointed out that our result is about series expansion of Hardy inequality under the case $p=n$, which case is not considered by Gkikas and Psaradakis in [K. T. Gkikas and G. Psaradakis. Optimal non-homogeneous improvements for the series expansion of Hardy's inequality. Commun. Contemp. Math. doi:10.1142/S0219199721500310]. However, we can't obtain the optimal form by our method.