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Interpolation of Besov spaces

Authors: Ronald A. DeVore and Vasil A. Popov
Journal: Trans. Amer. Math. Soc. 305 (1988), 397-414
MSC: Primary 46E35; Secondary 41A15, 46M35
MathSciNet review: 920166
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Abstract: We investigate Besov spaces and their connection with dyadic spline approximation in $ {L_p}(\Omega )$, $ 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.

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Keywords: Besov spaces, real interpolation spaces, dyadic splines, degree of approximation
Article copyright: © Copyright 1988 American Mathematical Society