Universal extension operator

Lev Kapitanski

University of Miami, Coral Gables, USA

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.

Keywords: Sobolev spaces, Besov spaces, Triebel–Lizorkin spaces, trace theorems, heat equation.

MSC: 46E35, 46F10, 35K05

Received: 17.03.2025
Revised: 24.04.2025
Accepted: 25.04.2025

DOI: 10.4213/faa4306

 English version: Functional Analysis and Its Applications, 2025, 59:3, 271–276

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