Representation and approximation of multivariate functions with mixed smoothness by hyperbolic wavelets

In this paper, we study the representation theorems of multivariate functions with mixed smoothness by wavelet basis formed by tensor products of univariate wavelets, we also study the best approximation in the Lq (Rd ) metric for some function classes with mixed smoothness by hyperbolic wavelets and obtain some asymptotic estimates of approximating order.  2003 Elsevier Inc. All rights reserved