6 problems

Let $n\geq2$ and $\frac12<s<\frac n2$. Let $(f_j)_j$ be an orthonormal system in $H^s(\mathbb{R}^n)$, and let $\beta$ be the exponent in the maximal estimate denoted by … holds for…

Let $n\geq2$, $q\geq \frac{2(n+1)}{n-1}$, and let $(f_j)_j$ be an orthonormal system in the homogeneous Sobolev space $\dot{H}^s(\mathbb{R}^n)$. For a sequence of coefficients…

Let $n\geq2$, let $(1/p,1/q)$ lie on the line segment $(O,A]$, and set $s$ by … For an orthonormal family $\{f_j\}_{j\in J}\subset\dot{H}^{s}(\mathbb{R}^n)$ and coefficients…

Let $n\geq1$, and let $A=(1/p,1/q)=((n-1)/(n+1),n/(n+1))$. For an orthonormal family $\{f_j\}_{j\in J}\subset L^2(\mathbb{R}^n)$ and a sequence…

Let $2\le q<p<\infty$, and let $\Phi$ be a finite, uniformly bounded orthonormal system. For a finite collection $\Theta$ of functions, define $K_p^*(\Theta)$ to be the smallest co…

Restricted-type endpoint conjecture. The estimate