Improved hardy and rellich type inequalities with two weight functions

Semra Ahmetolan; Ismail Kombe

doi:10.7153/mia-2018-21-60

Improved 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

1 Citation (Scopus)

Abstract

In this work, we obtain several improved versions of two weight Hardy and Rellich type inequalities on the sub-Riemannian manifold R²n+¹ defined by the vector fields ∂ ∂ X_j = _{∂ x j} + 2ky _j |z|²k−² _∂ ^∂ _l , Y_j = _{∂ y j} − 2kx _j |z|²k−² _∂ ^∂ _l , j = 1, 2,..., n where (z, l) = (x, y, l) ∈ R²n+¹ , |z| = (|x|² + |y|² )¹/² and k 1 .

Original language	English
Pages (from-to)	885-896
Number of pages	12
Journal	Mathematical Inequalities and Applications
Volume	21
Issue number	3
DOIs	https://doi.org/10.7153/mia-2018-21-60
Publication status	Published - Jul 2018

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© 2018 Element D.O.O. All rights reserved.

Keywords

Improved hardy inequality with two weight functions
Improved rellich inequality with two weight functions

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10.7153/mia-2018-21-60

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abstract = "In this work, we obtain several improved versions of two weight Hardy and Rellich type inequalities on the sub-Riemannian manifold R2n+1 defined by the vector fields ∂ ∂ Xj = ∂ x j + 2ky j |z|2k−2 ∂ ∂ l , Yj = ∂ y j − 2kx j |z|2k−2 ∂ ∂ l , j = 1, 2,..., n where (z, l) = (x, y, l) ∈ R2n+1 , |z| = (|x|2 + |y|2 )1/2 and k 1 .",

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AB - In this work, we obtain several improved versions of two weight Hardy and Rellich type inequalities on the sub-Riemannian manifold R2n+1 defined by the vector fields ∂ ∂ Xj = ∂ x j + 2ky j |z|2k−2 ∂ ∂ l , Yj = ∂ y j − 2kx j |z|2k−2 ∂ ∂ l , j = 1, 2,..., n where (z, l) = (x, y, l) ∈ R2n+1 , |z| = (|x|2 + |y|2 )1/2 and k 1 .

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ER -

Improved hardy and rellich type inequalities with two weight functions

Abstract

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Keywords

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