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

Li, Songxiao; Stević, Stevo

Indian J. Math. 50, No. 1, 177-188 (2008).

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 \(H_{p,q,\gamma}(B_1(0))\).

Reviewer: Niels Jacob (Swansea)

MSC:

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

Keywords:

Stieltjes transform; Riemann-Stieltjes operators; Bloch space; mixed norm spaces; boundedness; compactness of operators