Riemann–Stieltjes operators between \(\alpha\)-Bloch spaces and Besov spaces. (English) Zbl 1176.47024
This paper studies two Riemann–Stieltjes operators \(J_g\) and \(I_g\) on the unit disk
\[ J_gf(z)=\int_0^z f(\xi)g'(\xi)\,d\xi,\;I_gf(z)=\int_0^z f'(\xi)g(\xi)\,d\xi. \]
They are Toeplitz–Hankel type operators. The paper gives necessary and sufficient conditions for the boundedness and compactness of these two operators between the Besov space and \(\alpha\)-Besov space.
\[ J_gf(z)=\int_0^z f(\xi)g'(\xi)\,d\xi,\;I_gf(z)=\int_0^z f'(\xi)g(\xi)\,d\xi. \]
They are Toeplitz–Hankel type operators. The paper gives necessary and sufficient conditions for the boundedness and compactness of these two operators between the Besov space and \(\alpha\)-Besov space.
Reviewer: Lizhong Peng (Beijing)
MSC:
| 47B35 | Toeplitz operators, Hankel operators, Wiener-Hopf operators |
| 30H05 | Spaces of bounded analytic functions of one complex variable |
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