On a conjecture about contractive inequalities for weighted Bergman spaces

Abstract

We are interested in the norm of the inclusion between the standard weighted Bergman spaces $A_{\alpha }^2$ and $A_{\frac{p}{2}(\alpha +2)-2}^p$, $p>2$, which is conjectured to be contractive by O.F. Brevig, J. Ortega-Cerdà, K. Seip and J. Zhao (in the limit case $\alpha =-1$) and E. Lieb and J.P. Solovej (for $\alpha >-1$). We provide some partial answers and improvements of some recent results.

14 pages. 1 figure