On local fractal functions in Besov and Triebel-Lizorkin spaces

详细信息    查看全文

• 作者：Peter R. Massopust^a ; ^b ; ^{massopust@ma.tum.de" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Local iterated function system ; Fractal interpolation ; Read&ndash ; Bajraktarević operator ; Besov and Triebel&ndash ; Lizorkin spaces ; Local Hardy space ; Pointwise multiplier
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2016
• 出版时间：1 April 2016
• 年：2016
• 卷：436
• 期：1
• 页码：393-407
• 全文大小：402 K

文摘

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.