A NEW PROOF OF THE GAGLIARDO–NIRENBERG AND SOBOLEV INEQUALITIES: HEAT SEMIGROUP APPROACH

Tohru Ozawa; Taiki Takeuchi

doi:10.1090/bproc/211

A NEW PROOF OF THE GAGLIARDO–NIRENBERG AND SOBOLEV INEQUALITIES: HEAT SEMIGROUP APPROACH

Tohru Ozawa, Taiki Takeuchi

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

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^q estimate of the heat semigroup. For the Sobolev inequality, we consider another approach by using the heat semigroup and the Hardy inequality.

Original language	English
Pages (from-to)	371-377
Number of pages	7
Journal	Proceedings of the American Mathematical Society, Series B
Volume	11
DOIs	https://doi.org/10.1090/bproc/211
Publication status	Published - 2024
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis
Algebra and Number Theory
Geometry and Topology
Discrete Mathematics and Combinatorics

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10.1090/bproc/211

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title = "A NEW PROOF OF THE GAGLIARDO–NIRENBERG AND SOBOLEV INEQUALITIES: HEAT SEMIGROUP APPROACH",

abstract = "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 Lp-Lq estimate of the heat semigroup. For the Sobolev inequality, we consider another approach by using the heat semigroup and the Hardy inequality.",

keywords = "Gagliardo–Nirenberg inequality, Sobolev inequality, heat semigroup",

author = "Tohru Ozawa and Taiki Takeuchi",

note = "Publisher Copyright: {\textcopyright} 2024 by the author(s).",

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journal = "Proceedings of the American Mathematical Society, Series B",

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AU - Takeuchi, Taiki

PY - 2024

Y1 - 2024

N2 - 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 Lp-Lq estimate of the heat semigroup. For the Sobolev inequality, we consider another approach by using the heat semigroup and the Hardy inequality.

AB - 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 Lp-Lq estimate of the heat semigroup. For the Sobolev inequality, we consider another approach by using the heat semigroup and the Hardy inequality.

KW - Gagliardo–Nirenberg inequality

KW - Sobolev inequality

KW - heat semigroup

UR - https://www.scopus.com/pages/publications/85199799458

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SP - 371

EP - 377

JO - Proceedings of the American Mathematical Society, Series B

JF - Proceedings of the American Mathematical Society, Series B

ER -

A NEW PROOF OF THE GAGLIARDO–NIRENBERG AND SOBOLEV INEQUALITIES: HEAT SEMIGROUP APPROACH

Abstract

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