Affiliation:
1. Department of Mathematics, Indian Institute of Science, Bangalore 560012, India
Abstract
We are concerned with finding a class of weight functions g so that the following generalized Hardy-Sobolev inequality holds: ∫Ωgu2≤C∫Ω|∇u|2, u∈H01(Ω), for some C>0, where Ω is a bounded domain in ℝ2. By making use of Muckenhoupt condition for the one-dimensional weighted Hardy inequalities, we identify a rearrangement invariant Banach function space so that the previous integral inequality holds for all weight functions in it. For weights in a subspace of this space, we show that the best constant in the previous inequality is attained. Our method gives an alternate way of proving the Moser-Trudinger embedding and its refinement due to Hansson.
Funder
University Grants Commission
Cited by
6 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. On global bifurcation for the nonlinear Steklov problems;Topological Methods in Nonlinear Analysis;2021-12-05
2. On a reverse Hölder inequality for Schrödinger operators;Archiv der Mathematik;2021-11-26
3. On weighted logarithmic-Sobolev & logarithmic-Hardy inequalities;Journal of Mathematical Analysis and Applications;2021-04
4. Admissible function spaces for weighted Sobolev inequalities;Communications on Pure & Applied Analysis;2021
5. On the generalized Hardy-Rellich inequalities;Proceedings of the Royal Society of Edinburgh: Section A Mathematics;2019-01-26