We show that the d-dimensional Haar system H^d on the unit cube I^d is a Schauder basis in the classical Besov space B^s_p,q,1(I^d), 0 < p < 1, defined by first order ......

We reconsider some estimates from the 1994 paper [6] concerning the hierarchical basis preconditioner for sparse grid discretizations. The improvement is in three directions: We consider arbitrary space dimensions d > 1, ......

We determine all cases for which the d-dimensional Haar wavelet system H^d on the unit cube I^d is a conditional or unconditional Schauder basis in the classical isotropic Besov function spaces ......

On the example of the simplest C⁰ spline quarklet construction of [1], we demonstrate the possible reduction of the complexity estimates for the approximation of singularity functions on the unit interval given ......