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Function spaces of varying smoothness I
Author(s) -
Schneider Jan
Publication year - 2007
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200610580
Subject(s) - smoothness , mathematics , pointwise , function space , connection (principal bundle) , pure mathematics , function (biology) , wavelet , sequence (biology) , space (punctuation) , mathematical analysis , geometry , computer science , genetics , evolutionary biology , artificial intelligence , biology , operating system
This paper deals with function spaces of varying smoothness. It is a modified version of corresponding parts of [8]. Corresponding spaces of positive smoothness s ( x ) will be considered in part II. We define the spaces B , s 0p (ℝ n ), where the function : x ↦ s ( x ) is negative and determines the smoothness pointwise. First we prove basic properties and then we use different wavelet decompositions to get information about the local smoothness behavior. The main results are characterizations of the spaces B , s 0p (ℝ n ) by weighted sequence space norms of the wavelet coefficients. These assertions are used to prove an interesting connection to the so‐called two‐microlocal spaces C s , s ′ ( x 0 ). (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)