MÖBIUS INVARIANT FUNCTION SPACES and DIRICHLET SPACES with SUPERHARMONIC WEIGHTS

Guanlong Bao; Javad Mashreghi; Stamatis Pouliasis; Hasi Wulan

doi:10.1017/S1446788718000022

MÖBIUS INVARIANT FUNCTION SPACES and DIRICHLET SPACES with SUPERHARMONIC WEIGHTS

Guanlong Bao, Javad Mashreghi, Stamatis Pouliasis, Hasi Wulan

Mathematics and Statistics

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

4 Scopus citations

Abstract

Let D_μ be Dirichlet spaces with superharmonic weights induced by positive Borel measures μ on the open unit disk. Denote by M (D_μ) Möbius invariant function spaces generated by D_μ. In this paper, we investigate the relation among D_μ, M (D_μ) and some Möbius invariant function spaces, such as the space BMOA of analytic functions on the open unit disk with boundary values of bounded mean oscillation and the Dirichlet space. Applying the relation between BMOA and M (D_μ), under the assumption that the weight function K is concave, we characterize the function K such that Q_K = BMOA . We also describe inner functions in M (D_μ) spaces.

Original language	English
Pages (from-to)	1-18
Number of pages	18
Journal	Journal of the Australian Mathematical Society
Volume	106
Issue number	1
DOIs	https://doi.org/10.1017/S1446788718000022
State	Published - Feb 1 2019

Keywords

Dirichlet spaces with superharmonic weights
Möbius invariant function spaces
inner functions

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10.1017/S1446788718000022

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title = "M{\"O}BIUS INVARIANT FUNCTION SPACES and DIRICHLET SPACES with SUPERHARMONIC WEIGHTS",

abstract = "Let Dμ be Dirichlet spaces with superharmonic weights induced by positive Borel measures μ on the open unit disk. Denote by M (Dμ) M{\"o}bius invariant function spaces generated by Dμ. In this paper, we investigate the relation among Dμ, M (Dμ) and some M{\"o}bius invariant function spaces, such as the space BMOA of analytic functions on the open unit disk with boundary values of bounded mean oscillation and the Dirichlet space. Applying the relation between BMOA and M (Dμ), under the assumption that the weight function K is concave, we characterize the function K such that QK = BMOA . We also describe inner functions in M (Dμ) spaces.",

keywords = "Dirichlet spaces with superharmonic weights, M{\"o}bius invariant function spaces, inner functions",

author = "Guanlong Bao and Javad Mashreghi and Stamatis Pouliasis and Hasi Wulan",

note = "Funding Information: G. Bao and H. Wulan were supported by the NNSF of China (No. 11720101003). G. Bao was also supported by the STU Scientific Research Foundation for Talents (No. NTF17020). Publisher Copyright: {\textcopyright} 2018 Australian Mathematical Publishing Association Inc.",

year = "2019",

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doi = "10.1017/S1446788718000022",

language = "English",

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journal = "Journal of the Australian Mathematical Society",

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T1 - MÖBIUS INVARIANT FUNCTION SPACES and DIRICHLET SPACES with SUPERHARMONIC WEIGHTS

AU - Bao, Guanlong

AU - Mashreghi, Javad

AU - Pouliasis, Stamatis

AU - Wulan, Hasi

N1 - Funding Information: G. Bao and H. Wulan were supported by the NNSF of China (No. 11720101003). G. Bao was also supported by the STU Scientific Research Foundation for Talents (No. NTF17020). Publisher Copyright: © 2018 Australian Mathematical Publishing Association Inc.

PY - 2019/2/1

Y1 - 2019/2/1

N2 - Let Dμ be Dirichlet spaces with superharmonic weights induced by positive Borel measures μ on the open unit disk. Denote by M (Dμ) Möbius invariant function spaces generated by Dμ. In this paper, we investigate the relation among Dμ, M (Dμ) and some Möbius invariant function spaces, such as the space BMOA of analytic functions on the open unit disk with boundary values of bounded mean oscillation and the Dirichlet space. Applying the relation between BMOA and M (Dμ), under the assumption that the weight function K is concave, we characterize the function K such that QK = BMOA . We also describe inner functions in M (Dμ) spaces.

AB - Let Dμ be Dirichlet spaces with superharmonic weights induced by positive Borel measures μ on the open unit disk. Denote by M (Dμ) Möbius invariant function spaces generated by Dμ. In this paper, we investigate the relation among Dμ, M (Dμ) and some Möbius invariant function spaces, such as the space BMOA of analytic functions on the open unit disk with boundary values of bounded mean oscillation and the Dirichlet space. Applying the relation between BMOA and M (Dμ), under the assumption that the weight function K is concave, we characterize the function K such that QK = BMOA . We also describe inner functions in M (Dμ) spaces.

KW - Dirichlet spaces with superharmonic weights

KW - Möbius invariant function spaces

KW - inner functions

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U2 - 10.1017/S1446788718000022

DO - 10.1017/S1446788718000022

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AN - SCOPUS:85049585039

SN - 1446-7887

VL - 106

SP - 1

EP - 18

JO - Journal of the Australian Mathematical Society

JF - Journal of the Australian Mathematical Society

IS - 1

ER -

MÖBIUS INVARIANT FUNCTION SPACES and DIRICHLET SPACES with SUPERHARMONIC WEIGHTS

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Keywords

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