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Abstract <p> A new linear extension operator which extends (generalized) functions on a hyperplane in a Euclidean space to the whole space is introduced. It is shown that this operator is continuous as an operator between appropriate function spaces for a large class of Sobolev–Slobodetsky, Besov, and Triebel–Lizorkin spaces. </p>

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Universal Extension Operator

  • 期刊论文

  • 发表日期：

    2025年9月1日

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  • Lev Kapitanski

摘要

Abstract

A new linear extension operator which extends (generalized) functions on a hyperplane in a Euclidean space to the whole space is introduced. It is shown that this operator is continuous as an operator between appropriate function spaces for a large class of Sobolev–Slobodetsky, Besov, and Triebel–Lizorkin spaces.