| 6 | CHARACTERIZATION OF HLDER SPACES CORRESPONDING TO DITZIAN-TOTIK MODULUS OF SMOOTHNESS显示文摘For the step-weight function , we prove that the Holder spaces ∧a,p on the interval [-1,1], defined in terms of moduli of smoothness with the step-weight function ,are linearly isomorphic to some sequence spaces, and the isomorphism is given by the cofficients of function with respect to a system of orthonormal splines with knots uniformly distributed according to the measure with density . In case ∧a,p is contained in the space of continuous functions, we give a discrete characterization of this space, using only values of function at the appropriate knots. Application of these results to characterize the order of polynomial approximation is presented. | Anna Kamont(Mathematical Institute of the Polish Academy of Sciences ul. Abrahama 1881-825 Sopot, Poland e-mail: A. Kamont@impan. gda. pl) | 2000 | Analysis in Theory and Applications2000，16，1： | 0 |
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