Multilevel characterizations of anisotropic function spaces
AuthorKyriazis, George C.
SourceSIAM Journal on Mathematical Analysis
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We present a general method for extending decomposition systems of L 2(ℝd) to decomposition systems for the anisotropic Triebel-Lizorkin and Besov spaces, Fp,qα,s and Bp,qα,s, respectively, for the full range of the indexes. Our approach is based on techniques from harmonic analysis and relies on the boundedness of almost diagonal operators on appropriate sequence spaces. Typical examples of such decomposition systems are the various wavelet-type unconditional bases for L2(ℝd). © 2004 Society for Industrial and Applied Mathematics.