Refinements of q-Berezin radius inequalities

We present refinements of q-Berezin radius inequalities for bounded linear operators on reproducing kernel Hilbert spaces. Using the Berezin number, the Berezin–Crawford number, the Berezin norm, and the quantity $$\\widetilde{m}(P),$$ we derive upper bounds whose coefficient functions remain bounded on [0, 1]. One of these bounds is no larger than an earlier adapted estimate for every admissible value of q, while the estimate involving $$\\widetilde{m}(P)$$ may be sharper under an explicit condition. We also obtain inequalities for products of operators, including an application of Buzano’s inequality. Concrete examples demonstrate both the improvement over previously adapted estimates and the sharpness of certain RKHS-adapted linear inequalities.