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Function spaces of varying smoothness I

✍ Scribed by Jan Schneider

Publisher
John Wiley and Sons
Year
2007
Tongue
English
Weight
286 KB
Volume
280
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

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~p~ (ℝ^n^ ), where the function 𝕊: 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~p~ (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)

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