This article is cited in 1 scientific paper (total in 1 paper)
Weighted Sobolev-type embedding theorems for functions with symmetries
S. V. Ivanova, A. I. Nazarovb
a St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
b Saint-Petersburg State University
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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St. Petersburg Mathematical Journal, 2007, 18:1, 77–88
MSC: Primary 46E35; Secondary 58D99
S. V. Ivanov, A. I. Nazarov, “Weighted Sobolev-type embedding theorems for functions with symmetries”, Algebra i Analiz, 18:1 (2006), 108–123; St. Petersburg Math. J., 18:1 (2007), 77–88
Citation in format AMSBIB
\by S.~V.~Ivanov, A.~I.~Nazarov
\paper Weighted Sobolev-type embedding theorems for functions with symmetries
\jour Algebra i Analiz
\jour St. Petersburg Math. J.
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