Traces of weighted function spaces: Dyadic norms and Whitney extensions

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2017,（11）
• 页码范围: 1981-2010
• 页数: 30页
• 语种: 英文
• DOI: 10.1007/s11425-017-9148-6

摘要

The trace spaces of Sobolev spaces and related fractional smoothness spaces have been an active area of research since the work of Nikolskii,Aronszajn,Slobodetskii,Babich and Gagliardo among others in the 1950's.In this paper,we review the literature concerning such results for a variety of weighted smoothness spaces.For this purpose,we present a characterization of the trace spaces (of fractional order of smoothness),based on integral averages on dyadic cubes,which is well-adapted to extending functions using the Whitney extension operator.