@article{Qiu2026, 
author = {Xiu-Liang Qiu and Mehmet Gürdal and Selim Çetin and Ömer Kişi and Qing-Bo Cai},
title = {Spectral estimates for multiparametric operator products via the        A  -Berezin norm in RKHS},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {3},
pages = {6217-6230},
keywords = {Berezin number, reproducing kernel Hilbert space, semi-inner product, A-Berezin number, multiparametric inequalities, Schatten-type exponents},
url = {https://www.sciopen.com/article/10.3934/math.2026256},
doi = {10.3934/math.2026256},
abstract = {This paper addresses the spectral analysis of operators acting on reproducing kernel Hilbert spaces equipped with a semi-inner product induced by a positive operator        A  . A fundamental challenge in this setting is the geometric discrepancy between the normalized reproducing kernels and the unit        A  -sphere, which renders classical numerical radius techniques inapplicable. By overcoming this structural obstacle, we establish sharp inequalities for the        A  -Berezin number and        A  -Berezin norm. Our main contribution involves the derivation of multiparametric estimates for triple operator products of the form              P              α        X            R              α       involving Schatten-type exponents. These results generalize and refine existing bounds in the literature. Furthermore, we provide a qualitative analysis of the obtained bounds through weighted Toeplitz operators on Hardy spaces and verify the theoretical findings with concrete matrix examples involving the geometric behavior of weight functions.}
}