Wavelet decompositions of anisotropic Besov spaces

In this paper we develop the natural multiresolution analysis framework related to anisotropic Besov spaces B(p,q)(alpha)(R(n)). We prove two new Jackson and Bernstein type inequalities for these spaces, and obtain from well-known techniques [12, 7] new norm equivalences in terms of weighted sums of the wavelet coefficients. This provides a characterization for B(p,q)(alpha)(R(n)) (and for its dual) by means of compactly supported wavelets, which may be applied to the numerical resolution of semi-elliptic differential equations.