Mityagin's extension problem. Progress report

详细信息    查看全文

• 作者：Alexander Goncharov ; ^{goncha@fen.bilkent.edu.tr} ; Zeliha Ural ^{zeliha.ural@bilkent.edu.tr}
• 关键词：Whitney functions ; Extension problem ; Hausdorff measures ; Markov's factors
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 April 2017
• 年：2017
• 卷：448
• 期：1
• 页码：357-375
• 全文大小：542 K
• 卷排序：448

文摘

Given a compact set K⊂RdK⊂Rd, let E(K)E(K) denote the space of Whitney jets on K. The compact set K   is said to have the extension property if there exists a continuous linear extension operator W:E(K)⟶C∞(Rd)W:E(K)⟶C∞(Rd). In 1961 B.S. Mityagin posed a problem to give a characterization of the extension property in geometric terms. We show that there is no such complete description in terms of densities of Hausdorff contents or related characteristics. Also the extension property cannot be characterized in terms of growth of Markov's factors for the set.