4 problems

Consider the upper half-plane $\mathbb{R}_{+}^2=\{z\in\mathbb{C}:\operatorname{Im}z>0\}$, two weights $\mu_1$ and $\mu_2$ on $\mathbb{R}_{+}^2$, and the two-weight inequality … Her…

Let $T$ be a sparse operator, let $1<p<q<\infty$, and let $\mathcal{D}_{p,p}$ and $\mathcal{D}^{\ast}_{p,p}$ denote the corresponding direct comparison bump quantities for the case…

Let $T$ be a vector of standard singular integrals in higher dimensions, and suppose that $T$ is both strongly elliptic and strongly gradient elliptic. The energy conditions are th…

Let … mathbb{R}$. For each interval$I$, define the Poisson integral by … Let$b_I$be the unique, if it \exists, point such that … Let$\widetilde\sigma_I:=\sigma-\sigma{b_I}\del…