Scaling invariant Hardy inequalities of multiple logarithmic type on the whole space

Shuji Machihara; Tohru Ozawa; Hidemitsu Wadade

doi:10.1186/s13660-015-0806-1

Scaling invariant Hardy inequalities of multiple logarithmic type on the whole space

Shuji Machihara, Tohru Ozawa, Hidemitsu Wadade^*

^*Corresponding author for this work

School of Advanced Science and Engineering

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

13 Citations (Scopus)

Abstract

In this paper, we establish Hardy inequalities of logarithmic type involving singularities on spheres in Rⁿ in terms of the Sobolev-Lorentz-Zygmund spaces. We prove it by absorbing singularities of functions on the spheres by subtracting the corresponding limiting values.

Original language	English
Article number	281
Journal	Journal of Inequalities and Applications
Volume	2015
Issue number	1
DOIs	https://doi.org/10.1186/s13660-015-0806-1
Publication status	Published - 2015 Dec 25

Keywords

Sobolev-Lorentz-Zygmund space
best constant
logarithmic Hardy inequality
scaling invariant space

ASJC Scopus subject areas

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

Access to Document

10.1186/s13660-015-0806-1

Cite this

@article{f691d5c617844cc185be0b27e9671e9c,

title = "Scaling invariant Hardy inequalities of multiple logarithmic type on the whole space",

abstract = "In this paper, we establish Hardy inequalities of logarithmic type involving singularities on spheres in Rn in terms of the Sobolev-Lorentz-Zygmund spaces. We prove it by absorbing singularities of functions on the spheres by subtracting the corresponding limiting values.",

keywords = "Sobolev-Lorentz-Zygmund space, best constant, logarithmic Hardy inequality, scaling invariant space",

author = "Shuji Machihara and Tohru Ozawa and Hidemitsu Wadade",

note = "Publisher Copyright: {\textcopyright} 2015, Machihara et al.",

year = "2015",

month = dec,

day = "25",

doi = "10.1186/s13660-015-0806-1",

language = "English",

volume = "2015",

journal = "Journal of Inequalities and Applications",

issn = "1025-5834",

publisher = "Springer Publishing Company",

number = "1",

}

TY - JOUR

T1 - Scaling invariant Hardy inequalities of multiple logarithmic type on the whole space

AU - Machihara, Shuji

AU - Ozawa, Tohru

AU - Wadade, Hidemitsu

PY - 2015/12/25

Y1 - 2015/12/25

N2 - In this paper, we establish Hardy inequalities of logarithmic type involving singularities on spheres in Rn in terms of the Sobolev-Lorentz-Zygmund spaces. We prove it by absorbing singularities of functions on the spheres by subtracting the corresponding limiting values.

AB - In this paper, we establish Hardy inequalities of logarithmic type involving singularities on spheres in Rn in terms of the Sobolev-Lorentz-Zygmund spaces. We prove it by absorbing singularities of functions on the spheres by subtracting the corresponding limiting values.

KW - Sobolev-Lorentz-Zygmund space

KW - best constant

KW - logarithmic Hardy inequality

KW - scaling invariant space

UR - http://www.scopus.com/inward/record.url?scp=84942098688&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84942098688&partnerID=8YFLogxK

U2 - 10.1186/s13660-015-0806-1

DO - 10.1186/s13660-015-0806-1

M3 - Article

AN - SCOPUS:84942098688

SN - 1025-5834

VL - 2015

JO - Journal of Inequalities and Applications

JF - Journal of Inequalities and Applications

IS - 1

M1 - 281

ER -

Scaling invariant Hardy inequalities of multiple logarithmic type on the whole space

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this