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K-State Today

February 3, 2015

Mathematics Colloquium lecture Feb. 3

By Reta McDermott

Lizaveta Ihnatsyeva, University of Jyvskyl, will present "Extension and Trace Problems for Besov and Triebel-Lizorkin Functions" as part of the mathematics department Colloquium lecture series at 2:30 p.m. Tuesday, Feb. 3, in 122 Cardwell Hall.

The abstract for the lecture:
In the talk we first discuss some characterizations of the traces of functions from classical Besov spaces and Triebel-Lizorkin spaces to Ahlfors regular subsets of the Euclidean space, for instance, to some Cantor-type sets and self-similar sets. Recently there have been introduced several analogues for Besov spaces and Triebel-Lizorkin spaces in a quite general setting, which, in particular, includes certain topological manifolds, fractals, graphs and Carnot-Carathéodory spaces. Employing one of the available definitions, we give a characterization of extension domains for Besov-type and for Triebel-Lizorkin type functions in the setting of a metric measure space with a doubling measure; as a special case we obtain a characterization of extension domains for classical Besov spaces defined via Lp-modulus of smoothness. The talk is based on joint work with Antti Vähäkangas and joint work with Toni Heikkinen and Heli Tuominen.