Interpolation of Besov Spaces

Abstract

We investigate Besov spaces and their connection with dyadic spline approximation in <!-- MATH ${L_p}(\Omega )$ --> , <!-- MATH $0 < p \leqslant \infty$ --> <img width="99" height="37" align="MIDDLE" border="0" src="images/img7.gif" alt="$ 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.