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Riemann–Stieltjes operators between mixed norm spaces. (English) Zbl 1159.47012

In this paper, the authors study the boundedness and compactness of the Riemann–Stieltjes operators
\[ T_g f(z)= \int^1_0 f(tz)\operatorname{Re} g(tz)\,{dt\over t} \] and
\[ L_g f(z)= \int^1_0 \operatorname{Re}f(tz) g(tz)\,{dt\over t}, \]
where \(g: B_1(0)\to \mathbb{C}\) is a holomorphic mapping and \(z\in B_1(0)\). The interest is in the mapping properties between different mixed norm spaces of holomorphic functions \(H_{p,q,\gamma}(B_1(0))\).

MSC:

47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators
30H05 Spaces of bounded analytic functions of one complex variable
47G10 Integral operators
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