TY - JOUR
T1 - Sobolev inequalities with symmetry
AU - Cho, Yonggeun
AU - Ozawa, Tohru
PY - 2009/6
Y1 - 2009/6
N2 - In this paper, we derive some Sobolev inequalities for radially symmetric functions in s with 1/2 < s < n/2. We show the end point case s = 1/2 on the homogeneous Besov space B2,11/2. These results are extensions of the well-known Strauss' inequality [13]. Also non-radial extensions are given, which show that compact embeddings are possible in some Lp spaces if a suitable angular regularity is imposed.
AB - In this paper, we derive some Sobolev inequalities for radially symmetric functions in s with 1/2 < s < n/2. We show the end point case s = 1/2 on the homogeneous Besov space B2,11/2. These results are extensions of the well-known Strauss' inequality [13]. Also non-radial extensions are given, which show that compact embeddings are possible in some Lp spaces if a suitable angular regularity is imposed.
KW - Angular regularity.
KW - Function space with radial symmetry
KW - Sobolev inequality
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U2 - 10.1142/S0219199709003399
DO - 10.1142/S0219199709003399
M3 - Article
AN - SCOPUS:68049124964
VL - 11
SP - 355
EP - 365
JO - Communications in Contemporary Mathematics
JF - Communications in Contemporary Mathematics
SN - 0219-1997
IS - 3
ER -