Singular Integral Operators and the T(1) Theorem

Abstract: 

In the field of operator theory, seeking necessary and sufficient conditions for the LpLp-boundedness of large families of linear operators is quite a challenge in general.  However, boundedness is an analytically vital property to have, being one of the most fundamental regularity properties that an operator can possess. The family of singular integral operators is one which has seen a rich history in the field of harmonic analysis. 

This fact makes the T(1)T(1) theorem all the more impressive, since it provides a short list of simple, yet necessary and sufficient, conditions for the L2L2-boundedness of singular integral operators. We shall discuss some of the history and ideas surrounding this theorem.