5 problems

For each integer $d>2$, let $p^* = \frac{2d}{d-2}$. Determine whether there exists a constant $C_d<\infty$ such that, for all $f,g\in L^2(\mathbb{R}^d)$, the Born–Jordan distributi…

Local boundedness conjecture. Under these hypotheses, $u\in L^\infty(B_1)$.

Optimal logarithmic power conjecture. If $K'<\infty$, then there is a constant $C=C(s_1,\dots,s_n,p,n,d,\psi)$ such that every $f\in\mathscr C_0^\infty(\mathbb R^n)$ satisfies

Let $1\leq p_1,\dots,p_m<\infty$ and define $p$ by … Let $w_1,\dots,w_m$ and $\nu$ be weights such that $(w_1,\dots,w_m,\nu)\in A_{\vec P}^{\mathcal R}$, and let $v$ be a weight sa…

Weighted Lorentz dispersive estimates conjecture. For every $\alpha\ne0$ and $y\in\mathbb{R}^3$, one has