Gagliardo-Nirenberg 和 Sobolev 不等式的新证明：热半群方法

Proceedings of the American Mathematical Society, Series B Pub Date : 2024-07-11 DOI:10.1090/bproc/211

Tohru Ozawa, Taiki Takeuchi

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引用次数: 0

摘要

我们给出了基于热半群的 Gagliardo-Nirenberg 和 Sobolev 不等式的新证明。关于 Gagliardo-Nirenberg 不等式，我们仅依靠热半群的 L p L^p - L q L^q 估计值简化了之前的证明。对于索博廖夫不等式，我们考虑使用热半群和哈代不等式的另一种方法。

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A new proof of the Gagliardo–Nirenberg and Sobolev inequalities: Heat semigroup approach

We give a new proof of the Gagliardo–Nirenberg and Sobolev inequalities based on the heat semigroup. Concerning the Gagliardo–Nirenberg inequality, we simplify the previous proof by relying only on the L p L^p - L q L^q estimate of the heat semigroup. For the Sobolev inequality, we consider another approach by using the heat semigroup and the Hardy inequality.

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来源期刊

Proceedings of the American Mathematical Society, Series B

CiteScore

1.60

自引率

0.00%

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