| Abstract : In the talk we will present a simple introduction to the Bellman function technique - a powerful tool in harmonic analysis. This method the harmonic analysis "borrowed" from the applied mathematics, more precisely from the control theory. The power of this technique lies in its simplicity, which means it can be applied to many different problems. This method is also very good at finding sharp constants in many inequalities, in fact in many cases it is the only known method for finding these constants. We will demonstrate this technique at a simple model problem - the Carleson imbedding thorem. At the end we will present our results we obtained using the Bellman method. |