**"****Derivative-Free Characterization of **

**Harmonic
Besov Spaces****"**

By

**HAKKI TURGAY KAPTANOĞLU**

**(BİLKENT UNIVERSITY)**

**Abstract: ** This is a presentation of a recent paper of
Adem Ersin \"Ureyen to appear in the Journal of Mathematical
Analysis and Applications. The starting point is an estimate of the oscillation
of the
reproducing kernels of harmonic Besov spaces b_q^p on the unit ball of R^n for
q>-n. This leads to several characterizations of harmonic Besov spaces in a large region of p and q. They are
mostly in the form of the finiteness of a weighted double integral of some kind
of difference quotient of the functions. In a certain way, the region of
p and q considered is the largest possible.

**Date: ****Wednesday, November 4, 2015**

**Time: ****14:00**

**Place: ****Mathematics Seminar Room,
SA-141**

Tea and cookies will be served before the
seminar.