TY - JOUR

T1 - Weighted sobolev-type embedding theorems for functions with symmetries

AU - Иванов, Сергей Владимирович

AU - Nazarov, A. I.

PY - 2007/1/1

Y1 - 2007/1/1

N2 - 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 M and a compact group of isometries G. They showed that the limit Sobolev exponent increases if there are no points in M with discrete orbits under the action of G. In the paper, the situation where M contains points with discrete orbits is considered. It is shown that the limit Sobolev exponent for (Formula Presented) increases in the case of embeddings into weighted spaces Lq(M, w) instead of the usual Lq 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 (Formula Presented) into weighted Hölder and Orlicz spaces are treated.

AB - 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 M and a compact group of isometries G. They showed that the limit Sobolev exponent increases if there are no points in M with discrete orbits under the action of G. In the paper, the situation where M contains points with discrete orbits is considered. It is shown that the limit Sobolev exponent for (Formula Presented) increases in the case of embeddings into weighted spaces Lq(M, w) instead of the usual Lq 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 (Formula Presented) into weighted Hölder and Orlicz spaces are treated.

KW - Embedding theorems

KW - Sobolev spaces

KW - Symmetries

UR - http://www.scopus.com/inward/record.url?scp=85009775692&partnerID=8YFLogxK

U2 - 10.1090/S1061-0022-06-00943-5

DO - 10.1090/S1061-0022-06-00943-5

M3 - Article

AN - SCOPUS:85009775692

VL - 18

SP - 77

EP - 88

JO - St. Petersburg Mathematical Journal

JF - St. Petersburg Mathematical Journal

SN - 1061-0022

IS - 1

ER -