Abstract
Sobolev spaces with weights taking infinite values at some interior points of a two-dimensional domain are considered. For functions from these spaces, a Hardy inequality is obtained. Embedding theorems for weighted Lebesgue spaces and equivalent renorming theorems are proved.
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References
G. Hardy, J. Littlewood, and G. Polya, Inequalities (Cambridge Univ. Press, Cambridge, 1934; Inostrannaya Literatura, Moscow, 1948).
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Timerbaev M.R., “Spaces with a graph norm and strengthened Sobolev spaces, I,” Russian Math. (Iz. VUZ) 47(5), 52–62 (2004).
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Original Russian Text © M.R. Timerbaev, N.V. Timerbaeva, 2012, published in Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2012, Vol. 154, No. 3, pp. 173–179.
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Timerbaev, M.R., Timerbaeva, N.V. A Hardy inequality with a point-singular weight inside a domain. Lobachevskii J Math 34, 406–411 (2013). https://doi.org/10.1134/S1995080213040069
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DOI: https://doi.org/10.1134/S1995080213040069