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On local fractal functions in Besov and Triebel-Lizorkin spaces.
J. Math. Anal. Appl. 436, 393-407 (2016)
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, Hölder, Bessel potential, and local Hardy spaces.
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Publication type
Article: Journal article
Document type
Scientific Article
Keywords
Besov And Triebel-lizorkin Spaces ; Fractal Interpolation ; Local Hardy Space ; Local Iterated Function System ; Pointwise Multiplier ; Read-bajraktarević Operator; Construction; Surfaces
ISSN (print) / ISBN
0022-247X
e-ISSN
1096-0813
Quellenangaben
Volume: 436,
Issue: 1,
Pages: 393-407
Publisher
Elsevier
Publishing Place
San Diego
Non-patent literature
Publications
Reviewing status
Peer reviewed
Institute(s)
Institute of Computational Biology (ICB)