10 problems

Let ${\mathcal{A}}_p({\omega},{\sigma})$ denote the two-weight Muckenhoupt condition, and let the testing conditions be … for every cube $I$, where $\mathfrak{T}$ and…

Separated bump conjecture. One should have

Let $b^{\alpha,n}$ denote an elliptic vector of standard $b$-fractional singular integrals in $b^n$, acting between weighted spaces $L^2(\mathbb{R}^n;\sigma)$ and…

Let $b^{\alpha,n}$ denote an elliptic vector of standard $b$-fractional singular integrals in $b^n$, and let $b$ and $b$ be weights. The notation $\mathcal{A}_2^\alpha$ denotes the…

Let $b$ and $b$ be weights on $b^n$, let $H$ be the Hilbert transform, and let $b_Q$ denote the two-tailed auxiliary function associated with a cube $Q$. Write $b_Q$ and $b_Q$ for…

Let $\mathbf{T}^{\alpha,n}$ denote an elliptic vector of standard $\alpha$-fractional singular integrals in $\mathbb{R}^{n}$, and let $\sigma$ and $\omega$ be measures on…

Let $\tau$! be a pair of nonnegative locally finite measures $\tau=(\sigma,\omega)$ on $\mathbb{R}^{n}$, let $H$ be the Hilbert transform, and let…

Let $\rho$ and $v$ be general weights on the unit circle, and consider the two-weight Riesz projection … Let $\mathcal{P}$ denote the Poisson extension. The joint invariant $A_2$ c…

Let $1<p<\frac{\infty}{ }$, let $A$ and $B$ be Young functions, and let $\bar A$ and $\bar B$ denote their complementary Young functions. For a cube $Q$, write $\|\cdot\|_{A,Q}$ an…

Testing-condition conjecture. The two-weight inequality