I’m intrigued by the beginning of a new series of posts at the Everything Seminar about harmonic analysis. This particular post talks about the relationship of singular integral operators and Carleson’s Theorem. Carleson’s Theorem (that Fourier series of functions in *L ^{p}* for

*p > 1*converge pointwise almost everywhere) is a famously difficult result; the post gives some idea of where the difficulty lies.

For the ambitious, a complete proof is available in a preprint by Michael Lacey.