The existence of a bounded linear extension operator for L^s,p(ℝⁿ) when (n)/(p)<\s\

2024/10/09 by Han Li, Li, Han
Mathematics · #Holomorphic and Operator Theory #Differential Equations and Boundary Problems #Algebraic and Geometric Analysis

paper · pdf · doi:10.48550/arxiv.2410.07367

Abstract

Let L^s,p(ℝⁿ) denote the homogeneous Sobolev-Slobodeckij space. In this paper, we demonstrate the existence of a bounded linear extension operator from the jet space J^{\lfloor s \rfloor}_E L^s,p(ℝⁿ) to L^s,p(ℝⁿ) for any E ⊆ ℝⁿ, p ∈ [1, ∞), and s ∈ (0, ∞) satisfying (n)/(p) &lt; \s\, where \s\ represents the fractional part of s. Our approach builds upon the classical Whitney extension operator and uses the method of exponentially decreasing paths.

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