TY - JOUR
T1 - Besov spaces on open sets
AU - Iwabuchi, Tsukasa
AU - Matsuyama, Tokio
AU - Taniguchi, Koichi
N1 - Funding Information:
The first author was supported by Grant-in-Aid for Young Scientists Research (B) (No. 25800069), Japan Society for the Promotion of Science. The second author was supported by Grant-in-Aid for Scientific Research (C) (No. 15K04967), Japan Society for the Promotion of Science.
Publisher Copyright:
© 2019 Elsevier Masson SAS
PY - 2019/5
Y1 - 2019/5
N2 - This paper is devoted to giving definitions of Besov spaces on an arbitrary open set Ω of 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.
AB - This paper is devoted to giving definitions of Besov spaces on an arbitrary open set Ω of 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.
KW - Besov spaces
KW - Potential of Kato class
KW - Schrödinger operators
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U2 - 10.1016/j.bulsci.2019.01.008
DO - 10.1016/j.bulsci.2019.01.008
M3 - Article
AN - SCOPUS:85060718824
VL - 152
SP - 93
EP - 149
JO - Bulletin des Sciences Mathematiques
JF - Bulletin des Sciences Mathematiques
SN - 0007-4497
ER -