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On a conjecture about contractive inequalities for weighted Bergman spaces
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abstract
We are interested in the norm of the inclusion between the standard weighted Bergman spaces $A^2_\alpha$ and $A^p_{\frac{p}{2} (\alpha + 2)-2}$, $p > 2$, which is conjectured to be contractive by O.F. Brevig, J. Ortega-Cerd\`a, 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.
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Embedding and compact embedding between Bergman and Hardy spaces
The paper gives the full if-and-only-if characterization of embeddings and compact embeddings between Hardy and weighted Bergman spaces on the unit ball for all exponents and weights.
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