Sharp estimates for operators with positive Bergman kernel in Homogeneous Siegel domains of Cn

TL;DR

This paper establishes precise conditions for the boundedness of operators with positive Bergman kernels in certain homogeneous Siegel domains of Cn, improving upon previous tests like the Schur test using the Okikiolu test.

Contribution

It provides necessary and sufficient conditions for L^p-boundedness of these operators, utilizing the Okikiolu test for sharper results.

Findings

Derived exact L^p-boundedness criteria

Improved upon Schur test results

Applied Okikiolu test for sharper estimates

Abstract

We obtain necessary and sufficient conditions for the $L^p$-boundedness of the operator with positive Bergman kernel in some homogeneous Siegel domains of Cn. The key tool used here is the Okikiolu test, which finally leads to better result than the Schur test as it has been used so far.