5 problems

Quotient-space decay conjecture. The spaces $\mathcal L^{1'}_v$ and $\mathcal L'_v$ possess the same decay properties as $\mathcal L^1_v$ and $\mathcal L_v$, respectively. The sour…

Weighted decay conjecture. There exists $\delta>0$ such that $h_L\in\mathcal L^1_{\tau_\delta}$. If true, this would support identifying $\mathcal L^1$ with a union of the weighted…

Let $\nu$ be a finite positive Borel measure on $[0,1]$, let $T_\nu:L^p(\mathbb{D})\to L^q(\mathbb{D})$ be the associated Shimorin-type operator, and let $\mathcal{C}$ be the bound…

Let $\nu$ be a finite positive Borel measure on $[0,1]$, and let $T_\nu:L^p(\mathbb{D})\to L^q(\mathbb{D})$ be the associated Shimorin-type operator. Define … where $c'$ is the dua…

Let $(X,d,\mu)$ be a bounded metric measure space with kernel $K$ and associated operator $T_K\colon L^2(X,\mu)\to L^2(X,\mu)$. Let $(X,d,\mu_n)$ have analogous kernel $K_n$ and op…