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On local fractal functions in Besov and Triebel-Lizorkin spaces.

J. Math. Anal. Appl. 436, 393-407 (2016)
Postprint DOI
Open Access Green
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 Article Number: , Supplement: ,
Publisher Elsevier
Publishing Place San Diego
Reviewing status Peer reviewed