Abstract
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 VBp,qδ,w(Rd) whose smoothness includes normal Besov spaces, Besov spaces with dominating mixed smoothness, and their interpolation. Furthermore, we obtain wavelet characterization of VBp,qδ,w(Rd). 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.
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