5 problems

Let $C_{\alpha}$ denote the maximally modulated oscillatory singular integral operator considered in the paper, and let its $L^p$ constants mean the constants in the corresponding…

Let $d\in\mathbb{N}$, and for a real-coefficient polynomial $P$ of degree at most $d$ define the polynomial Carleson operator by … Here $\operatorname{p.v.}$ denotes the principal…

Konyagin's conjecture. The Lorentz space

Let $f\in L\log\log L(\mathbb T)$, and let $(n_j)$ be a lacunary sequence of integers, meaning that there is some $\theta>1$ such that $n_{j+1}\geq\theta n_j$ for every $j$. Write…

The $L\log L$ conjecture. A natural reformulation of the almost-everywhere Fourier-convergence conjecture is that condition $$ holds for ${mathcal C}$ with