Weighted estimates of the Bergman projection with matrix weights. (English) Zbl 07861160
Condori, Alberto A. (ed.) et al., Recent progress in function theory and operator theory. AMS special session, virtual, April 6, 2022. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 799, 53-73 (2024).
Summary: We establish a weighted inequality for the Bergman projection with matrix weights for a class of pseudoconvex domains. We extend a result of A. Aleman and O. Constantin [J. Funct. Anal. 262, No. 5, 2359–2378 (2012; Zbl 1247.46022)] and obtain the following estimate for the weighted norm of \(P\):
\[
\Vert P\Vert_{L^2(\Omega,W)}\leq C(\mathcal{B}_2(W))^{2}.
\]
Here \(\mathcal{B}_2(W)\) is the Bekollé-Bonami constant for the matrix weight \(W\) and \(C\) is a constant that is independent of the weight \(W\) but depends upon the dimension and the domain.
For the entire collection see [Zbl 1542.47001].
For the entire collection see [Zbl 1542.47001].
MSC:
| 32A25 | Integral representations; canonical kernels (Szegő, Bergman, etc.) |
| 32A36 | Bergman spaces of functions in several complex variables |
| 32A50 | Harmonic analysis of several complex variables |
| 42B20 | Singular and oscillatory integrals (Calderón-Zygmund, etc.) |
| 42B35 | Function spaces arising in harmonic analysis |
Citations:
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