Multivariate Haar systems in Besov function spaces

02/28/2020

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by   Peter Oswald, et al.

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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<∞, 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 H̃^d, and characterize the parameter range for which the dual of B_p,q,1^s(I^d) is trivial for 0<p<1.