6 problems

Let $alpha>-1$ and let $w\buttonin B_{1,alpha}$ be a weight on the unit disc. Write $[w]_{B_{1,alpha}}$ for its $B_{1,alpha}$-constant, and let $P_{alpha}$ denote the Bergman proje…

Let $\omega$ be a radial weight and let $1<p<\infty$. Denote by $L^p_\omega$ the radial weighted $L^p$ space and by $P_\omega$ the Bergman projection associated with $\omega$. Berg…

Kalaj and Marković's conjecture.

Let $P$ be the Bergman projection on the unit disk. For $1<p<\infty$, let $q:=p/(p-1)$ be the conjugate exponent and let $\|P\|_p$ denote the operator norm of $P$ on…

Let $P$) denote the Bergman projection on the unit disk, and for $1<p<\infty$ let $\|P\|_p$ be its operator norm on $L^p(\mathbb{D})$. Dostanić's conjecture. Dostanić conjectured t…

Power-improved two-weight conjecture. If $(\mu_1^r,\mu_2^r)\in A_p^+(\mathbb{R}_{+}^2)$ for some $r>1$, then the displayed inequality holds for some $C>0$. This is presented as a v…