ノイ　タカヒロ   Noi Takahiro   野井　貴弘    所属   追手門学院大学  大学所属    職種   講師
発行・発表の年月	2022
形態種別	論文
査読	査読あり
標題	Wavelet Characterization of Local Muckenhoupt Weighted Sobolev Spaces with Variable Exponents
執筆形態	共著・編著（代表編著を除く）
掲載誌名	Constructive Approximation
掲載区分	国外
著者・共著者	Mitsuo Izuki,Toru Nogayama,Takahiro Noi,Yoshihiro Sawano
概要	The goal of this paper is to define local weighted variable Sobolev spaces of fractional and negative order and their characterization by wavelets. We first consider local weighted variable Sobolev spaces by means of weak derivatives and obtain a wavelet characterization for these spaces. Using the Bessel potentials, we next define local weighted variable Sobolev spaces of fractional order. We show that Sobolev spaces obtained by weak derivatives and those by the Bessel potentials coincide. Finally, using duality, we define local weighted variable Sobolev spaces with negative order. We also show that local weighted variable Sobolev spaces are closed under complex interpolation. Some examples are given including the applications to weighted uniformly local Lebesgue spaces with variable exponents and periodic function spaces as a by-product, although the exponent is constant.
DOI	10.1007/s00365-022-09573-6
ISSN	0176-4276/1432-0940