## On tangential Fatou property

- March 24, 2005
- 2 p.m.
- LeConte 312

## Abstract

Celebrated Fatou Theorem states the existence almost everywhere of nontangential limit for a bounded harmonic function in the unit disc. Well-known Littlewood example demonstrates that nontangential approach cone cannot be replaced by any rotation invariant tangential region. Rudin proved that nontangential approach in Fatou Theorem can be changed to the not-nontangential if one allows the shape of approach region to vary from point to point. He asked a question whether this can be true for certain tangential regions. In the talk a solution to Rudin's problem will be provided. Also, some quantitative version of the Fatou Theorem will be discussed.