Geodesic
Weighted Sobolev-type embedding theorems for functions with symmetries
Algebra i analiz, Tome 18 (2006) no. 1, pp. 108-123 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is well known that Sobolev embeddings can be refined in the presence of symmetries. Hebey and Vaugon (1997) studied this phenomena in the context of an arbitrary Riemannian manifold $\mathcal M$ and a compact group of isometries $G$. They showed that the limit Sobolev exponent increases if there are no points in $\mathcal M$ with discrete orbits under the action of $G$. In the paper, the situation where $\mathcal M$ contains points with discrete orbits is considered. It is shown that the limit Sobolev exponent for $W_p^1(\mathcal M)$ increases in the case of embeddings into weighted spaces $L_q(\mathcal M,w)$ instead of the usual $L_q$ spaces, where the weight function $w(x)$ is a positive power of the distance from $x$ to the set of points with discrete orbits. Also, embeddings of $W_p^1(\mathcal M)$ into weighted Hölder and Orlicz spaces are treated. 
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     title = {Weighted {Sobolev-type} embedding theorems for functions with symmetries},
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     url = {http://geodesic.mathdoc.fr/item/AA_2006_18_1_a3/}
}
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S. V. Ivanov; A. I. Nazarov. Weighted Sobolev-type embedding theorems for functions with symmetries. Algebra i analiz, Tome 18 (2006) no. 1, pp. 108-123. http://geodesic.mathdoc.fr/item/AA_2006_18_1_a3/

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