Although numerous studies have focused on normal Besov spaces, limited studies have been conducted on exponentially weighted Besov spaces. Therefore, we define exponentially weighted Besov space $VB_{p,q}^{\delta,w}(\mathbb{R}^d)$ whose smoothness includes normal Besov spaces, Besov spaces with dominating mixed smoothness, and their interpolation. Furthermore, we obtain wavelet characterization of $VB_{p,q}^{\delta,w}(\mathbb{R}^d)$. Next, approximation formulas such as sparse grids are derived using the determined formula. The results of this study are expected to provide considerable insight into the application of exponentially weighted Besov spaces with mixed smoothness.
翻译:尽管许多研究侧重于正常的贝索夫空间,但对指数加权贝索夫空间进行了有限的研究,因此,我们定义了指数加权贝索夫空间 $VB ⁇ p,q ⁇ delta,w}(\mathb{R ⁇ d),其平滑包括正常的贝索夫空间,占主导性混合平滑的贝索夫空间及其内插。此外,我们获得了对 $VB ⁇ p,q ⁇ delta,w}(\mathb{R ⁇ d) 的波盘定性。接下来,利用确定的公式得出了诸如稀少的网格等近似公式。本研究的结果预计将为指数加权贝索夫空间的应用提供相当的洞察力。