On local fractal functions in Besov and Triebel-Lizorkin spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:436

Article

Massopust, Peter R.^1,2 

[1] Tech Univ Munich, Res Unit M6, Ctr Math, Boltzmannstr 3, D-85747 Garching, Germany

[2] Helmholtz Zentrum Munchen, Landstr 1, D-8764 Neuherberg, Germany

关键词: Local iterated function system;    Fractal interpolation;    Read-Bajraktarevic operator;    Besov and Triebel-Lizorkin spaces;    Local Hardy space;    Pointwise multiplier;   

DOI  :  10.1016/j.jmaa.2015.12.019

来源: Elsevier

【 摘 要 】

Within the new concept of a local iterated function system (local IFS), we consider a class of attractors of such IFSs, namely those that are graphs of functions. These new functions are called local fractal functions and they extend and generalize those that are currently found in the fractal literature. For a class of local fractal functions, we derive explicit conditions for them to be elements of Besov and Triebel-Lizorkin spaces. These two scales of functions spaces play an important role in interpolation theory and for certain ranges of their defining parameters describe many classical function spaces (in the sense of equivalent norms). The conditions we derive provide immediate information about inclusion of local fractal functions in, for instance, Lebesgue, Sobolev, Slobodeckij, Holder, Bessel potential, and local Hardy spaces. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free