Abstract and Applied Analysis

Composition Operators from the Hardy Space to the Zygmund-Type Space on the Upper Half-Plane

Stevo Stević

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Abstract

Here we introduce the n th weighted space on the upper half-plane Π + = { z : I m z > 0 } in the complex plane . For the case n = 2 , we call it the Zygmund-type space, and denote it by 𝒵 ( Π + ) . The main result of the paper gives some necessary and sufficient conditions for the boundedness of the composition operator C φ f ( z ) = f ( φ ( z ) ) from the Hardy space H p ( Π + ) on the upper half-plane, to the Zygmund-type space, where φ is an analytic self-map of the upper half-plane.

Article information

Source
Abstr. Appl. Anal., Volume 2009 (2009), Article ID 161528, 8 pages.

Dates
First available in Project Euclid: 16 March 2010

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1268745549

Digital Object Identifier
doi:10.1155/2009/161528

Mathematical Reviews number (MathSciNet)
MR2501016

Zentralblatt MATH identifier
1173.30036

Citation

Stević, Stevo. Composition Operators from the Hardy Space to the Zygmund-Type Space on the Upper Half-Plane. Abstr. Appl. Anal. 2009 (2009), Article ID 161528, 8 pages. doi:10.1155/2009/161528. https://projecteuclid.org/euclid.aaa/1268745549


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