# Cocompact embeddings of function spaces

Seminar
Speaker
Prof. Cyril Tintarev, Uppsala, visiting Technion
Date
30/12/2019 - 15:45 - 14:00Add to Calendar 2019-12-30 14:00:00 2019-12-30 15:45:00 Cocompact embeddings of function spaces A sequence  in a Banach space $E$ is called $G$-weak convergent, relative to a set $G$ of homeomorphisms of $E$  if $\forall g_k \in G$, $g_k(u_k-u)\rightharpoonup 0$. An embedding of two Banach spaces is called $G$-cocompact if every $G$-weakly convergent sequence in $E$ is convergent in $F$. Cocompact embeddings allow to improve convergence of bounded sequences beyond weak convergence when there is no pertinent compactness. On a series of examples in Sobolev, Besov, Lorenz-Zygmund, and Stricharz spaces, we show how cocompactness follows from compactness via a suitable decomposition, for example the Littlewood-Paley decomposition or the wavelet expansion. 2nd floor Colloquium Room, Building 216 אוניברסיטת בר-אילן - המחלקה למתמטיקה mathoffice@math.biu.ac.il Asia/Jerusalem public
Place
2nd floor Colloquium Room, Building 216
Abstract

A sequence  in a Banach space $E$ is called $G$-weak convergent, relative to a set $G$
of homeomorphisms of $E$  if $\forall g_k \in G$, $g_k(u_k-u)\rightharpoonup 0$. An
embedding of two Banach spaces is called $G$-cocompact if every $G$-weakly convergent
sequence in $E$ is convergent in $F$. Cocompact embeddings allow to improve convergence
of bounded sequences beyond weak convergence when there is no pertinent compactness.
On a series of examples in Sobolev, Besov, Lorenz-Zygmund, and Stricharz spaces, we show
how cocompactness follows from compactness via a suitable decomposition, for example the
Littlewood-Paley decomposition or the wavelet expansion.

תאריך עדכון אחרון : 27/12/2019