A Note on Generalized Hardy-Sobolev Inequalities

T. V. Anoop

International Journal of Analysis, 2013, vol. 2013, 1-9

Abstract:

We are concerned with finding a class of weight functions so that the following generalized Hardy-Sobolev inequality holds: , for some , where is a bounded domain in . 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.

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:ijanal:784398

DOI: 10.1155/2013/784398

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