Abstract
In this paper, by using some classical Mulholland type inequality, Berezin symbols and reproducing kernel technique, we prove the power inequalities for the Berezin number $ber(A)$ for some self-adjoint operators $A$ on ${H}(\Omega )$. Namely, some Mulholland type inequality for reproducing kernel Hilbert space operators are established. By applying this inequality, we prove that $(ber(A))^{n}\leq C_{1}ber(A^{n})$ for any positive operator $A$ on ${H}(\Omega )$.
Highlights
If p > 1, p + q = 1, an, bn ≥ satisfy < ∞ m=2 m apm
By using some classical Mulholland type inequality, Berezin symbols and reproducing kernel technique, we prove the power inequalities for the Berezin number ber(A) for some self-adjoint operators A on H(Ω)
We prove that (ber(A))n ≤ C1ber(An) for any positive operator A on H(Ω)
Summary
By using some classical Mulholland type inequality, Berezin symbols and reproducing kernel technique, we prove the power inequalities for the Berezin number ber(A) for some self-adjoint operators A on H(Ω). Some Mulholland type inequality for reproducing kernel Hilbert space operators are established. We prove that (ber(A))n ≤ C1ber(An) for any positive operator A on H(Ω).
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