6 problems

Let $S\subset\mathbb{R}^n$ and let $C_c(\mathbb{R}^n)$ denote the compactly supported continuous functions on $\mathbb{R}^n$. A rigid motion of $\mathbb{R}^n$ is denoted by…

Let $\lambda$ be fixed, let $U_{\lambda}$ be the subgroup associated with $\lambda$, and let the Radon transform $\operatorname{\mathcal{R}}$ act on the complex-valued function spa…

Let $0\leq j<k\leq n-1$ satisfy $j+k=n-1$, and let $r>0$. Let $S(\Gamma_H(n,d))$ denote the space of rapidly decreasing smooth functions on the hyperbolic Grassmannian, with all de…

Let $n\ge 2$ and $1< p < \infty$. Let $M^{\beta}_*$ denote the generalized spherical maximal operator on $\mathbb{R}^n$, and let condition (cnd18) be … with the last inequality wea…

The sharp norm conjecture for the $(j,k)$-plane transform. One has

Let $F_q$ be a finite field, let $dgeq 2$ and $1\leq kleq d-1$ be integers, and let $T_{Pi_k}$ denote the $k$-plane transform on the collection $Pi_k$ of all $k$-planes in $F_q^d$,…