Zygmund Type Mean Lipschitz Spaces on the Unit Ball of ℂn

Ern Gun Kwon; Hong Rae Cho; Hyungwoon Koo

doi:10.1007/s11118-013-9382-5

Zygmund Type Mean Lipschitz Spaces on the Unit Ball of ℂⁿ

Ern Gun Kwon, Hong Rae Cho, Hyungwoon Koo

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

On the unit ball of ℂⁿ, the space of those holomorphic functions satisfying mean Lipschitz condition (Formula presented) is characterized by integral growth conditions of the tangential derivatives as well as the radial derivatives, where ω_p*(t, f) denotes the double difference L^p modulus of continuity defined in terms of the unitary transformations of ℂⁿ.

Original language	English
Pages (from-to)	543-553
Number of pages	11
Journal	Potential Analysis
Volume	41
Issue number	2
DOIs	https://doi.org/10.1007/s11118-013-9382-5
Publication status	Published - 2014 Jun

Keywords

Besov space
Mean Lipschitz condition
Mean modulus of continuity
Zygmund class

ASJC Scopus subject areas

Analysis

Access to Document

10.1007/s11118-013-9382-5

Cite this

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title = "Zygmund Type Mean Lipschitz Spaces on the Unit Ball of ℂn",

abstract = "On the unit ball of ℂn, the space of those holomorphic functions satisfying mean Lipschitz condition (Formula presented) is characterized by integral growth conditions of the tangential derivatives as well as the radial derivatives, where ωp*(t, f) denotes the double difference Lp modulus of continuity defined in terms of the unitary transformations of ℂn.",

keywords = "Besov space, Mean Lipschitz condition, Mean modulus of continuity, Zygmund class",

author = "Kwon, {Ern Gun} and Cho, {Hong Rae} and Hyungwoon Koo",

note = "Funding Information: Ern Gun Kwon was supported by NRF-2010-0021986. Hong Rae Cho was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government (NRF-2011-0013740). Hyungwoon Koo was supported by NRF-2012000705.",

year = "2014",

month = jun,

doi = "10.1007/s11118-013-9382-5",

language = "English",

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journal = "Potential Analysis",

issn = "0926-2601",

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T1 - Zygmund Type Mean Lipschitz Spaces on the Unit Ball of ℂn

AU - Kwon, Ern Gun

AU - Cho, Hong Rae

AU - Koo, Hyungwoon

N1 - Funding Information: Ern Gun Kwon was supported by NRF-2010-0021986. Hong Rae Cho was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government (NRF-2011-0013740). Hyungwoon Koo was supported by NRF-2012000705.

PY - 2014/6

Y1 - 2014/6

N2 - On the unit ball of ℂn, the space of those holomorphic functions satisfying mean Lipschitz condition (Formula presented) is characterized by integral growth conditions of the tangential derivatives as well as the radial derivatives, where ωp*(t, f) denotes the double difference Lp modulus of continuity defined in terms of the unitary transformations of ℂn.

AB - On the unit ball of ℂn, the space of those holomorphic functions satisfying mean Lipschitz condition (Formula presented) is characterized by integral growth conditions of the tangential derivatives as well as the radial derivatives, where ωp*(t, f) denotes the double difference Lp modulus of continuity defined in terms of the unitary transformations of ℂn.

KW - Besov space

KW - Mean Lipschitz condition

KW - Mean modulus of continuity

KW - Zygmund class

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DO - 10.1007/s11118-013-9382-5

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JO - Potential Analysis

JF - Potential Analysis

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