Interpolation of Besov spaces

Abstract

We investigate Besov spaces and their connection with dyadic spline approximation in L p ( Ω ) {L_p}(\Omega ) , 0 > p ⩽ ∞ 0 > p \leqslant \infty . Our main results are: the determination of the interpolation spaces between a pair of Besov spaces; an atomic decomposition for functions in a Besov space; the characterization of the class of functions which have certain prescribed degree of approximation by dyadic splines.