## Arkadiusz Lewandowski (03/11/14)

Math Colloquium

### Speaker: Arkadiusz Lewandowski, University of Iceland

Title: Separate vs joint regularity of functions

Location: V-157, VRII

Time: Monday, November 3 at 15:00-16:00.

### Abstract:

Consider the following problem:

Given two domains \(D \subset K^p, G \subset K^q\), where \(K\) equals either \(\mathbb R\) or \(\mathbb C\), and a function \(f\) on the product \(D \times G\), taking complex values, and such that:

1. \(f(a,-)\) is in \(F(G)\), for any \(a\) in \(D\),

2. \(f(-,b)\) is in \(F(D)\), for any \(b\) in \(G\),

we ask whether \(f\) is in \(F(D\times G)\).

Here for any open set \(U\) in any \(K^n, F(U)\) is some abstract family of functions.

We shall discus the cases \(F \in \{\mathcal{C,O,H,SH}\}\), where \(\mathcal C\) denotes the family of continuous functions, \(\mathcal O\) is the family of holomorphic functions, \(\mathcal H\) stands for the family of harmonic functions, and \(\mathcal{SH}\) – the family of subharmonic functions.