Functional Analysis and Applications Seminar 

13/02/2004, 15:00 — 16:00 — Room P3.10, Mathematics Building
Alexei Karlovich, Instituto Superior Técnico, U.T. Lisboa

Commutatorsof Singular Integrals on Variable \(L_p\) Spaces II

This talk is a continuation of the previous one by Andrei Lerner. We will show that if a function \(b\) belongs to the Zygmund space \(L\log L\) locally and the commutator \([b,T]\) with the Calderon-Zygmund operator \(T\) is bounded on the variable \(L_p\) space, then \(b\) is of bounded mean oscillation. This is a necessry part of our generalization of the Coifman-Rochberg-Weiss commutator theorem. Certainly, the variable exponent p in our theorem has to satisfy some (natural) assumptions. This talk is based on the joint work with Andrei Lerner (Bar-Ilan University, Israel).