REPRESENTATION FORMULAE FOR THE HIGHER-ORDER STEKLOV AND L2m-FRIEDRICHS INEQUALITIES∗

Tohru Ozawa; Durvudkhan Suragan

doi:10.4310/AJM.2024.v28.n1.a4

REPRESENTATION FORMULAE FOR THE HIGHER-ORDER STEKLOV AND L^2m-FRIEDRICHS INEQUALITIES^∗

Tohru Ozawa, Durvudkhan Suragan

School of Sciences and Humanities

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

Abstract

In this paper, we obtain remainder term representation formulae for the higherorder Steklov inequality for vector fields which imply short and direct proofs of the sharp (classical) Steklov inequalities. The obtained results directly imply sharp Steklov type inequalities for some vector fields satisfying Hörmander’s condition, for example. We also give representation formulae for the L^2m-Friedrichs inequalities for vector fields.

Original language	English
Pages (from-to)	93-102
Number of pages	10
Journal	Asian Journal of Mathematics
Volume	28
Issue number	1
DOIs	https://doi.org/10.4310/AJM.2024.v28.n1.a4
Publication status	Published - 2024

Keywords

Friedrichs inequality
remainder term
Steklov inequality
vector fields

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

Access to Document

10.4310/AJM.2024.v28.n1.a4

Cite this

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abstract = "In this paper, we obtain remainder term representation formulae for the higherorder Steklov inequality for vector fields which imply short and direct proofs of the sharp (classical) Steklov inequalities. The obtained results directly imply sharp Steklov type inequalities for some vector fields satisfying H{\"o}rmander{\textquoteright}s condition, for example. We also give representation formulae for the L2m-Friedrichs inequalities for vector fields.",

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