Bulletin of the Belgian Mathematical Society - Simon Stevin

Riemann-Stieltjes operators on Hardy spaces in the unit ball of $\mathbb C^n$

Songxiao Li and Stevo Stević

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Abstract

Let $g:B\to \mathbb C^1$ be a holomorphic map of the unit ball $B$. We study the integral operators $$ T_gf(z)=\int_0^1f(tz)\Re g(tz)\frac{dt}{t}; \ \ L_gf(z)= \int_0^1 \Re f(tz) g(tz)\frac{dt}{t},\qquad z\in B. $$ The boundedness and compactness of the operators $T_g$ and $L_g$ on the Hardy space $H^2$ in the unit ball are discussed in this paper.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 14, Number 4 (2007), 621-628.

Dates
First available in Project Euclid: 15 November 2007

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1195157131

Digital Object Identifier
doi:10.36045/bbms/1195157131

Mathematical Reviews number (MathSciNet)
MR2384458

Zentralblatt MATH identifier
1136.47023

Subjects
Primary: 47B38: Operators on function spaces (general)
Secondary: 32A35: Hp-spaces, Nevanlinna spaces [See also 32M15, 42B30, 43A85, 46J15]

Keywords
Riemann-Stieltjes operator Hardy space BMOA space

Citation

Li, Songxiao; Stević, Stevo. Riemann-Stieltjes operators on Hardy spaces in the unit ball of $\mathbb C^n$. Bull. Belg. Math. Soc. Simon Stevin 14 (2007), no. 4, 621--628. doi:10.36045/bbms/1195157131. https://projecteuclid.org/euclid.bbms/1195157131


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