Hardy and rellich type inequalities with two weight functions

Semra Ahmetolan; Ismail Kombe

doi:10.7153/mia-19-68

Hardy and rellich type inequalities with two weight functions

Semra Ahmetolan, Ismail Kombe

Department of Mathematics Engineering

Istanbul Ticaret University

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

3 Citations (Scopus)

Abstract

In the present paper we prove several sharp two-weight Hardy, Hardy-Poincaŕe, and Rellich type inequalities on the sub-Riemannian manifold R2n+1 = Rn x Rn xR defined by the vector fields: Xj = ∂ /∂ xj +2kyj |z|2k?2 ∂/ ∂ l Yj = ∂ /∂ yj ?2kxj |z|^2k?2∂/ ∂ l, j = 1,2, ..,n where (z,y) = (x,y, l) ∂ R²ⁿ⁺¹ , |z| = (|x|² +|y|²)^1/2 and k ≥ 1.

Original language	English
Pages (from-to)	937-948
Number of pages	12
Journal	Mathematical Inequalities and Applications
Volume	19
Issue number	3
DOIs	https://doi.org/10.7153/mia-19-68
Publication status	Published - Jul 2016

Keywords

Hardy inequality with two weight functions
Rellich inequality with two weight functions
Sharp constan

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title = "Hardy and rellich type inequalities with two weight functions",

abstract = "In the present paper we prove several sharp two-weight Hardy, Hardy-Poinca{\'r}e, and Rellich type inequalities on the sub-Riemannian manifold R2n+1 = Rn x Rn xR defined by the vector fields: Xj = ∂ /∂ xj +2kyj |z|2k?2 ∂/ ∂ l Yj = ∂ /∂ yj ?2kxj |z|2k?2∂/ ∂ l, j = 1,2, ..,n where (z,y) = (x,y, l) ∂ R2n+1 , |z| = (|x|2 +|y|2)1/2 and k ≥ 1.",

keywords = "Hardy inequality with two weight functions, Rellich inequality with two weight functions, Sharp constan",

author = "Semra Ahmetolan and Ismail Kombe",

year = "2016",

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AU - Kombe, Ismail

PY - 2016/7

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N2 - In the present paper we prove several sharp two-weight Hardy, Hardy-Poincaŕe, and Rellich type inequalities on the sub-Riemannian manifold R2n+1 = Rn x Rn xR defined by the vector fields: Xj = ∂ /∂ xj +2kyj |z|2k?2 ∂/ ∂ l Yj = ∂ /∂ yj ?2kxj |z|2k?2∂/ ∂ l, j = 1,2, ..,n where (z,y) = (x,y, l) ∂ R2n+1 , |z| = (|x|2 +|y|2)1/2 and k ≥ 1.

AB - In the present paper we prove several sharp two-weight Hardy, Hardy-Poincaŕe, and Rellich type inequalities on the sub-Riemannian manifold R2n+1 = Rn x Rn xR defined by the vector fields: Xj = ∂ /∂ xj +2kyj |z|2k?2 ∂/ ∂ l Yj = ∂ /∂ yj ?2kxj |z|2k?2∂/ ∂ l, j = 1,2, ..,n where (z,y) = (x,y, l) ∂ R2n+1 , |z| = (|x|2 +|y|2)1/2 and k ≥ 1.

KW - Hardy inequality with two weight functions

KW - Rellich inequality with two weight functions

KW - Sharp constan

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DO - 10.7153/mia-19-68

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SP - 937

EP - 948

JO - Mathematical Inequalities and Applications

JF - Mathematical Inequalities and Applications

IS - 3

ER -

Hardy and rellich type inequalities with two weight functions

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