5 problems

For $d\geq1$, let $\mathfrak{p}_d(q)$ be the critical exponent of the Riesz projection on $\mathbb{T}^d$, and let $\mathfrak{q}(d)$ be its minimal admissible exponent. Monotonicity…

Let $1<q<2$ or $2<q\leq\infty$, let $\mathfrak{p}(q)$ be the one-dimensional critical exponent, and let $P_+$ denote the Riesz projection on the unit circle. Extremizer conjecture.…

Critical exponent conjecture. One should have

For $1\leq p<\infty$, let $p'=\frac{p}{p-1}$, let $P_+$ denote the Riesz projection on $L^{p'}(\mathbb T)$, and let $H^{4/p}$ be the Hardy space with exponent $4/p$. Brevig–Ortega-…

Riesz projection contractivity conjecture. The operator $P$ is a contraction from $L^r(\mathbb{T})$ to $H^q$. In addition, for every $f\in L^1(\mathbb{T})$,