a R&D Group for Mathematical Modelling, Numerical Simulation and Computer Visualization, Institute for Information, Energy and Space Technology, Narvik University College, 2 Lodve Lange’s St., P.O.Box 385, Narvik N‐8505, NORWAY
b Department of Mathematics, Luleå University of Technology, SE‐97187 Luleå, SWEDEN
In this communication we study in detail the relations between the smoothness of f and
in the case when the smoothness of the univariate non‐negative functions f is measured via Besov and Triebel‐Lizorkin space scales. The results obtained can be considered also as embedding theorems for usual Besov and Triebel‐Lizorkin spaces and their analogues in Hellinger metric. These results can be used in constrained approximation using wavelets, with applications to probability density estimation in speech recognition, non‐negative non‐parametric regression‐function estimation in positron‐emission tomography
(PET) imaging, shape/order‐preserving and/or one‐sided approximation and many others.