Piecewise linear bases and Besov spaces on fractal sets
For a compact d-dimensional fractal subset \(F\) of \({\mathbf R^n}\) endowed with a Hausdorff measure and admitting a convenient sequence of triangulations (a number of examples of such sets are included in the paper), analogues of the Faber--Schauder and of the Franklin systems are described, and several applications to Besov spaces on this fractal set for a certain range of parameters are given. These applications include the construction of extension operators for pairs of sets \(G\subset F\), and the characterization of Besov spaces in terms of coefficients of functions with respect to wavelets bases.
scientific article; zbMATH DE number 1759076