It is relatively easy to show that the Carleson–Hunt theorem follows from the boundedness of the Carleson operator from Lp(R) to itself for 1 < p < ∞. However, proving that it is bounded is difficult, …

Lennart Carleson proved Luzin's conjecture that the Fourier series of each $f\in L^2 (0,2\pi)$ converges almost everywhere. Also, Richard Hunt extended the result to $L^p$ ($p>1$).

Jul 17, 2014 · For a function in $L_2 (0,2\pi)$ its trigonometric Fourier series converges almost everywhere. This was stated as a conjecture by N.N. Luzin [1] and proved by L. Carleson [2]. The …

This book contains a detailed exposition of Carleson-Hunt theorem following the proof of Carleson: to this day this is the only one giving better bounds. It points out the motivation of every step in the proof.

Theorem 2.3. The spaces ( ; ) and Lip( ; ) for 0 < < 1 are equivalent as Banach spaces that is ( ; ) = Lip( ; ) with MkfkB( ; ) kfk ( ; ) NkfkB( ; ), where M and N are absolute constants.

Jul 1, 2003 · We give a complete proof, following joint work of the author and C. Thiele. Over 20 exercises are also detailed. We also discuss the derviation of the theorem on L^p spaces. And …

The Carleson-Hunt theorem, a profound result in the field of harmonic analysis, addresses a fundamental question about the convergence of Fourier series. It establishes that for a square …

Feb 6, 2024 · Carleson's theorem is a fundamental result in mathematical analysis establishing the pointwise (Lebesgue) almost everywhere convergence of Fourier series of L2 functions, proved by …

Jul 2, 2011 · We will follow the Carleson's approach in this talk and discuss the iteration arguments and the construction of exceptional sets.

I've recently started to learn about Fourier series from Grafakos' Classical Fourier Analysis, and I just stumbled upon the Carleson-Hunt theorem. Besides being my new favorite theorem, I'd really like to …