Several Weighted Hardy, Hardy-Sobolev-Maz'ya and Related Inequalities

2021/08/10 by İsmail Kömbe, Kömbe, I., Sümeyye Bakim +3
Mathematics · #26D10 #35A23 #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2108.04522

openalex publication_date 2021/08/10 · openalex created_date 2021/08/16 · openalex updated_date 2026/07/28

Abstract

In this paper we establish several Hardy and Hardy-Sobolev type inequalities with homogeneous weights on the first orthant ℝ_*ⁿ:=\(x₁, …, x_n):x₁>0, …, x_n>0 \. We then use some of them to produce Hardy type inequalities with remainder terms. Furthermore, we obtain some interpolation inequalities and Maz'ya type inequalities with remainder terms with the help of Maz'ya inequality and Sobolev inequality of Cabré and Ros-Orton on the upper half space ℝ₊ⁿ:=\x=(x₁, …, x_n)| x_n>0 \.

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