Multivariate Haar systems in Besov function spaces

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 B-p,q,1(s)(I-d), 0 < p, q < infinity, 0 <= s < 1/p, defined in terms of first-order L-p-moduli of smoothness. We obtain similar results for the tensor-product Haar system <(H)over tilde>(d), and characterize the parameter range for which the dual of B-p,q,1(s) (I-d) is trivial for 0 < p < 1.