Hajłasz–Sobolev imbedding and extension

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• 作者：Yuan Zhou<sup>asup><sup> ; sup><sup>bsup><sup> ; sup><sup>1sup><sup> ; sup><sup>yuan.y.zhou@jyu.fi"" rel=""nofollowsup>
• 关键词：Haj&#x142 ; asz– ; Sobolev space ; Haj&#x142 ; asz– ; Sobolev extension ; Haj&#x142 ; asz– ; Sobolev imbedding ; Triebel– ; Lizorkin space ; Weak cigar domain ; Uniform domain ; Local linear connectivity
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2011
• 出版时间：15 October 2011
• 年：2011
• 卷：382
• 期：2
• 页码：577-593
• 全文大小：289 K

文摘

The author establishes some geometric criteria for a Haj&#x142;asz–Sobolev -extension (resp. -imbedding) domain of with n2, s(0,1] and p[n/s,∞] (resp. p(n/s,∞]). In particular, the author proves that a bounded finitely connected planar domain Ω is a weak α-cigar domain with α(0,1) if and only if for some/all s[α,1) and p=(2−α)/(s−α), where denotes the restriction of the Triebel–Lizorkin space on Ω.