Positive Toeplitz operators between the harmonic Bergman spaces

Boo Rim Choe; Hyungwoon Koo; Heungsu Yi

doi:10.1023/A:1016356229211

Positive Toeplitz operators between the harmonic Bergman spaces

Boo Rim Choe, Hyungwoon Koo, Heungsu Yi

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

34 Citations (Scopus)

Abstract

On the setting of the upper half space we study positive Toeplitz operators between the harmonic Bergman spaces. We give characterizations of bounded and compact positive Toeplitz operators taking a harmonic Bergman space b^p into another b^q for 1 < p < ∞, 1 < q < ∞. The case p = 1 or q = 1 seems more intriguing and is left open for further investigation. Also, we give criteria for positive Toeplitz operators acting on b² to be in the Schatten classes. Some applications are also included.

Original language	English
Pages (from-to)	307-335
Number of pages	29
Journal	Potential Analysis
Volume	17
Issue number	4
DOIs	https://doi.org/10.1023/A:1016356229211
Publication status	Published - 2002

Bibliographical note

Funding Information:
★ Supported by the research grant of Kwangwoon University (2000), the Korea University Grant (2001), KOSEF 2000-1-10100-001-3, and KOSEF 98-0701-03-01-5.

Keywords

Carleson measures
Half-space
Harmonic Bergman functions
Multipliers
Positive Toeplitz operators

ASJC Scopus subject areas

Analysis

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10.1023/A:1016356229211

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title = "Positive Toeplitz operators between the harmonic Bergman spaces",

abstract = "On the setting of the upper half space we study positive Toeplitz operators between the harmonic Bergman spaces. We give characterizations of bounded and compact positive Toeplitz operators taking a harmonic Bergman space bp into another bq for 1 < p < ∞, 1 < q < ∞. The case p = 1 or q = 1 seems more intriguing and is left open for further investigation. Also, we give criteria for positive Toeplitz operators acting on b2 to be in the Schatten classes. Some applications are also included.",

keywords = "Carleson measures, Half-space, Harmonic Bergman functions, Multipliers, Positive Toeplitz operators",

author = "Choe, {Boo Rim} and Hyungwoon Koo and Heungsu Yi",

note = "Funding Information: ★ Supported by the research grant of Kwangwoon University (2000), the Korea University Grant (2001), KOSEF 2000-1-10100-001-3, and KOSEF 98-0701-03-01-5.",

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doi = "10.1023/A:1016356229211",

language = "English",

volume = "17",

pages = "307--335",

journal = "Potential Analysis",

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T1 - Positive Toeplitz operators between the harmonic Bergman spaces

AU - Choe, Boo Rim

AU - Koo, Hyungwoon

AU - Yi, Heungsu

N1 - Funding Information: ★ Supported by the research grant of Kwangwoon University (2000), the Korea University Grant (2001), KOSEF 2000-1-10100-001-3, and KOSEF 98-0701-03-01-5.

PY - 2002

Y1 - 2002

N2 - On the setting of the upper half space we study positive Toeplitz operators between the harmonic Bergman spaces. We give characterizations of bounded and compact positive Toeplitz operators taking a harmonic Bergman space bp into another bq for 1 < p < ∞, 1 < q < ∞. The case p = 1 or q = 1 seems more intriguing and is left open for further investigation. Also, we give criteria for positive Toeplitz operators acting on b2 to be in the Schatten classes. Some applications are also included.

AB - On the setting of the upper half space we study positive Toeplitz operators between the harmonic Bergman spaces. We give characterizations of bounded and compact positive Toeplitz operators taking a harmonic Bergman space bp into another bq for 1 < p < ∞, 1 < q < ∞. The case p = 1 or q = 1 seems more intriguing and is left open for further investigation. Also, we give criteria for positive Toeplitz operators acting on b2 to be in the Schatten classes. Some applications are also included.

KW - Carleson measures

KW - Half-space

KW - Harmonic Bergman functions

KW - Multipliers

KW - Positive Toeplitz operators

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SN - 0926-2601

VL - 17

SP - 307

EP - 335

JO - Potential Analysis

JF - Potential Analysis

IS - 4

ER -

Positive Toeplitz operators between the harmonic Bergman spaces

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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