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The Haar System and Smoothness Spaces built on Morrey Spaces

Presented by: 
Winfried Sickel
Tuesday 19th February 2019 - 09:00 to 09:35
INI Seminar Room 1
For some  Nikol'skij-Besov spaces $B^s_{p,q}$ the orthonormal Haar system can be used as an unconditional Schauder basis. Nowadays necessary and sufficient conditions with respect to $p,q$ and $s$ are known for this property. In recent years in a number of papers some modifications of Nikol'skij-Besov spaces based on Morrey spaces have been investigated. In my talk I will concentrate on a version called Besov-type spaces and denoted by $B^{s,\tau}_{p,q}$. It will be my aim to discuss some necessary and some sufficient conditions on the parameters $p,q,s,\tau$ such that one can characterize these classes by means of the Haar system. This is joined work with Dachun Yang and Wen Yuan (Beijing Normal University).
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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons