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Function spaces on local fields. (English) Zbl 1113.46069
Summary: We study function spaces on local fields, such as Triebel $B$-type and $F$-type spaces, Hölder type spaces, Sobolev type spaces, etc. Moreover, we study the relationship between the $p$-type derivatives and the Hölder type spaces. Our results show that there exists quite a difference between the functions defined on Euclidean spaces and local fields, respectively. Furthermore, many properties of functions defined on local fields motivate the new idea of solving some important problems in fractal analysis.
##### MSC:
 46S10 Functional analysis over fields (not $ℝ$, $ℂ$, $ℍ$or quaternions) 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
##### References:
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