Hardy type inequalities with spherical derivatives

Neal Bez; Shuji Machihara; Tohru Ozawa

doi:10.1007/s42985-019-0001-1

Hardy type inequalities with spherical derivatives

Neal Bez, Shuji Machihara^*, Tohru Ozawa

^*Corresponding author for this work

School of Advanced Science and Engineering

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

3 Citations (Scopus)

Abstract

A Hardy type inequality is presented with spherical derivatives in Rⁿ with n≥ 2 in the framework of equalities. This clarifies the difference between contribution by radial and spherical derivatives in the improved Hardy inequality as well as nonexistence of nontrivial extremizers without compactness arguments.

Original language	English
Article number	5
Journal	Partial Differential Equations and Applications
Volume	1
Issue number	1
DOIs	https://doi.org/10.1007/s42985-019-0001-1
Publication status	Published - 2020 Feb

ASJC Scopus subject areas

Analysis
Applied Mathematics
Computational Mathematics
Numerical Analysis

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title = "Hardy type inequalities with spherical derivatives",

abstract = "A Hardy type inequality is presented with spherical derivatives in Rn with n≥ 2 in the framework of equalities. This clarifies the difference between contribution by radial and spherical derivatives in the improved Hardy inequality as well as nonexistence of nontrivial extremizers without compactness arguments.",

author = "Neal Bez and Shuji Machihara and Tohru Ozawa",

note = "Funding Information: The first author was supported by JSPS KAKENHI Grant number 16H05995 and 16K1377, the second author was supported by JSPS KAKENHI Grant number JP16K05191, the third author was supported by JSPS KAKENHI Grant number 19H00644 and 18KK0073. Publisher Copyright: {\textcopyright} 2020, Springer Nature Switzerland AG.",

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AU - Machihara, Shuji

AU - Ozawa, Tohru

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PY - 2020/2

Y1 - 2020/2

N2 - A Hardy type inequality is presented with spherical derivatives in Rn with n≥ 2 in the framework of equalities. This clarifies the difference between contribution by radial and spherical derivatives in the improved Hardy inequality as well as nonexistence of nontrivial extremizers without compactness arguments.

AB - A Hardy type inequality is presented with spherical derivatives in Rn with n≥ 2 in the framework of equalities. This clarifies the difference between contribution by radial and spherical derivatives in the improved Hardy inequality as well as nonexistence of nontrivial extremizers without compactness arguments.

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Hardy type inequalities with spherical derivatives

Abstract

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