期刊
JOURNAL OF FUNCTIONAL ANALYSIS
卷 195, 期 2, 页码 230-238出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1006/jfan.2002.3955
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The article is concerned with the Bourgain, Brezis and Mironescu theorem on the asymptotic behaviour of the norm of the Sobolev-type embedding operator: W-s,W-p --> Lpn/(n-sP) as s up arrow 1 and s up arrow n/p. Their result is extended to all values of s is an element of (0,1) and is supplied with an elementary proof. The relation lim(sdown arrow0)(s) integral(Rn)integral(Rn) \u(x)-u(y)\(p)/\x-y\(n+sp) dx dy = 2p(-1)\Sn-1\parallel touparallel to(Lp(Rn))(p) is proved. (C) 2002 Elsevier Science (USA).
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