# The Haar System and Smoothness Spaces built on Morrey Spaces

ASCW01 - Challenges in optimal recovery and hyperbolic cross approximation

For some  Nikol'skij-Besov spaces $Bs_{p,q}$ 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).

This talk is part of the Isaac Newton Institute Seminar Series series.