Wavelet characterizations for anisotropic Besov spaces (Q1599914)

The goal of this paper is to provide wavelet characterizations for anisotropic Besov spaces. Depending on the anisotropy, appropriate biorthogonal tensor product bases are introduced and Jackson and Bernstein estimates are proved for two--parameter families of finite dimensional spaces. These estimates lead to characterizations for anisotropic Besov spaces by anisotropy dependent linear approximation spaces and lead further on to interpolation and embedding results. Finally, wavelet characterizations for anisotropic Besov spaces with respect to \(L_p\) spaces with \(0 < p < \infty\), are derived.