Besov spaces on open sets

2016/03/04 by Tsukasa Iwabuchi, Iwabuchi, Tsukasa, Tokio Matsuyama +3
Mathematics · #30H25 #46F05 #81Q10 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:30H25 #msc:46F05 #msc:81Q10

paper · pdf · doi:10.48550/arxiv.1603.01334

arxiv created 2016/03/04 · arxiv updated 2016/03/07

Abstract

This paper is devoted to giving definitions of Besov spaces on an arbitrary open set of \mathbb Rⁿ via the spectral theorem for the Schrödinger operator with the Dirichlet boundary condition. The crucial point is to introduce some test function spaces on Ω. The fundamental properties of Besov spaces are also shown, such as embedding relations and duality, etc. Furthermore, the isomorphism relations are established among the Besov spaces in which regularity of functions is measured by the Dirichlet Laplacian and the Schrödinger operators.

Related

• Besov classes on finite- and infinite-dimensional spaces and embedding\n theorems
• Besov spaces in operator theory
• Besov spaces associated with the Harmonic oscillator
• Besov spaces for Schrodinger operators with barrier potentials
• Properties of parabolic Sobolev and parabolic Besov spaces