Riemann-Stieltjes Operators on \(F(p,q,s)\) and \(H(p,q,\phi)\) Spaces of the Unit Ball

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DOI: https://doi.org/10.28924/2291-8639-24-2026-170
Published: May 29, 2026
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M. Hassanlou, H. Gissy, Riemann-Stieltjes Operators on \(F(p,q,s)\) and \(H(p,q,\phi)\) Spaces of the Unit Ball, Int. J. Anal. Appl., 24 (2026), 170.

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M. Hassanlou, H. Gissy

Abstract

Let \(g , f\) be  holomorphic functions on the unit ball \(\mathbb{B}_n\) of the \(\mathbb{C}^n\). The Riemann--Stieltjes operator is defined by \[L_g f (z) = \int_0^1 \mathcal{R} f(tz) g(tz) \frac{dt}{t}, \ \ \ z \in \mathbb{B}_n,\] where \(\mathcal{R} f\) is the radial derivative of \(f\). The objective of this paper is to find an estimation for the essential norm of this operator from the spaces \(F(p,q,s)\) (general function space) and \(H(p,q,\phi)\) (mixed--norm space)  into Zygmund--type space in the unit ball of \(\mathbb{C}^n\). As applications we find compactness characterization for the above operator.

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