Wavelet Characterization of Local Muckenhoupt Weighted Sobolev Spaces with Variable Exponents
Wavelet Characterization of Local Muckenhoupt Weighted Sobolev Spaces with Variable Exponents
复制标题
DOI：
10.1007/s00365-022-09573-6
复制
发表时间：
2022-05
影响因子：
2.7
通讯作者：
M. Izuki;T. Nogayama;T. Noi;Y. Sawano
中科院分区：
文献类型：
--
作者：
M. Izuki;T. Nogayama;T. Noi;Y. Sawano
本文的目的是定义分数阶和负阶局部加权变Sobolev空间，并利用小波刻画它们。我们首先考虑局部加权变Sobolev空间的弱导数，并获得这些空间的小波特征。利用Bessel势，我们接下来定义分数阶的局部加权可变Sobolev空间。证明了由弱导数得到的Sobolev空间与由Bessel势得到的Sobolev空间是一致的。最后，利用对偶性，我们定义了具有负序的局部加权可变Sobolev空间。我们还证明了局部加权变Sobolev空间在复插值下是闭的。给出了一些例子，包括应用于加权一致局部Lebesgue空间与可变指数和周期函数空间作为副产品，虽然指数是常数。
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.