![](/images/graphics-bg.png)
A Note on Generalized Hardy-Sobolev Inequalities
Author
Source
International Journal of Analysis
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-01-08
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Anoop, T. V.. 2013. A Note on Generalized Hardy-Sobolev Inequalities. International Journal of Analysis،Vol. 2013, no. 2013, pp.1-9.
https://search.emarefa.net/detail/BIM-497826
Modern Language Association (MLA)
Anoop, T. V.. A Note on Generalized Hardy-Sobolev Inequalities. International Journal of Analysis No. 2013 (2013), pp.1-9.
https://search.emarefa.net/detail/BIM-497826
American Medical Association (AMA)
Anoop, T. V.. A Note on Generalized Hardy-Sobolev Inequalities. International Journal of Analysis. 2013. Vol. 2013, no. 2013, pp.1-9.
https://search.emarefa.net/detail/BIM-497826
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-497826