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

Matematik Bölümü

Istanbul Ticaret University

Araştırma sonucu: Dergiye katkı › Makale › bilirkişi

3 Atıf (Scopus)

Özet

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.

Orijinal dil	İngilizce
Sayfa (başlangıç-bitiş)	937-948
Sayfa sayısı	12
Dergi	Mathematical Inequalities and Applications
Hacim	19
Basın numarası	3
DOI'lar	https://doi.org/10.7153/mia-19-68
Yayın durumu	Yayınlandı - Tem 2016

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10.7153/mia-19-68

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Link to publication in Scopus

Alıntı Yap

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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",

month = jul,

doi = "10.7153/mia-19-68",

language = "English",

volume = "19",

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journal = "Mathematical Inequalities and Applications",

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T1 - Hardy and rellich type inequalities with two weight functions

AU - Ahmetolan, Semra

AU - Kombe, Ismail

PY - 2016/7

Y1 - 2016/7

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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U2 - 10.7153/mia-19-68

DO - 10.7153/mia-19-68

M3 - Article

AN - SCOPUS:84989918461

SN - 1331-4343

VL - 19

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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