Commutators on weighted Morrey spaces on spaces of homogeneous type

Ruming Gong; Ji Li; Elodie Pozzi; Manasa N. Vempati

doi:10.1515/agms-2020-0116

Commutators on weighted Morrey spaces on spaces of homogeneous type

Ruming Gong, Ji Li^*, Elodie Pozzi, Manasa N. Vempati

^*Corresponding author for this work

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

6 Citations (Scopus)

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Abstract

In this paper, we study the boundedness and compactness of the commutator of Calderón- Zygmund operators T on spaces of homogeneous type (X, d, μ) in the sense of Coifman and Weiss. More precisely, we show that the commutator [b, T] is bounded on the weighted Morrey space L_ω^p,k(X) with κ ∈ (0, 1) and ω ∈ Ap(X), 1 < p < ∞, if and only if b is in the BMO space. We also prove that the commutator [b, T] is compact on the same weighted Morrey space if and only if b belongs to the VMO space. We note that there is no extra assumptions on the quasimetric d and the doubling measure μ.

Original language	English
Pages (from-to)	305-334
Number of pages	30
Journal	Analysis and Geometry in Metric Spaces
Volume	8
Issue number	1
DOIs	https://doi.org/10.1515/agms-2020-0116
Publication status	Published - 2020

Bibliographical note

Copyright the Author(s) 2020. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.

Keywords

commutator
compact operator
BMO space
VMO space
weighted Morrey space
space of homogeneous type

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10.1515/agms-2020-0116Licence: CC BY

Publisher version (open access)Final published version, 622 KBLicence: CC BY

Cite this

@article{a8206ba79e5b442393840537cffee09d,

title = "Commutators on weighted Morrey spaces on spaces of homogeneous type",

abstract = "In this paper, we study the boundedness and compactness of the commutator of Calder{\'o}n- Zygmund operators T on spaces of homogeneous type (X, d, μ) in the sense of Coifman and Weiss. More precisely, we show that the commutator [b, T] is bounded on the weighted Morrey space Lωp,k(X) with κ ∈ (0, 1) and ω ∈ Ap(X), 1 < p < ∞, if and only if b is in the BMO space. We also prove that the commutator [b, T] is compact on the same weighted Morrey space if and only if b belongs to the VMO space. We note that there is no extra assumptions on the quasimetric d and the doubling measure μ. ",

keywords = "commutator, compact operator, BMO space, VMO space, weighted Morrey space, space of homogeneous type",

author = "Ruming Gong and Ji Li and Elodie Pozzi and Vempati, {Manasa N.}",

note = "Copyright the Author(s) 2020. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.",

year = "2020",

doi = "10.1515/agms-2020-0116",

language = "English",

volume = "8",

pages = "305--334",

journal = "Analysis and Geometry in Metric Spaces",

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T1 - Commutators on weighted Morrey spaces on spaces of homogeneous type

AU - Gong, Ruming

AU - Li, Ji

AU - Pozzi, Elodie

AU - Vempati, Manasa N.

N1 - Copyright the Author(s) 2020. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.

PY - 2020

Y1 - 2020

N2 - In this paper, we study the boundedness and compactness of the commutator of Calderón- Zygmund operators T on spaces of homogeneous type (X, d, μ) in the sense of Coifman and Weiss. More precisely, we show that the commutator [b, T] is bounded on the weighted Morrey space Lωp,k(X) with κ ∈ (0, 1) and ω ∈ Ap(X), 1 < p < ∞, if and only if b is in the BMO space. We also prove that the commutator [b, T] is compact on the same weighted Morrey space if and only if b belongs to the VMO space. We note that there is no extra assumptions on the quasimetric d and the doubling measure μ.

AB - In this paper, we study the boundedness and compactness of the commutator of Calderón- Zygmund operators T on spaces of homogeneous type (X, d, μ) in the sense of Coifman and Weiss. More precisely, we show that the commutator [b, T] is bounded on the weighted Morrey space Lωp,k(X) with κ ∈ (0, 1) and ω ∈ Ap(X), 1 < p < ∞, if and only if b is in the BMO space. We also prove that the commutator [b, T] is compact on the same weighted Morrey space if and only if b belongs to the VMO space. We note that there is no extra assumptions on the quasimetric d and the doubling measure μ.

KW - commutator

KW - compact operator

KW - BMO space

KW - VMO space

KW - weighted Morrey space

KW - space of homogeneous type

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UR - http://purl.org/au-research/grants/arc/DP170101060

U2 - 10.1515/agms-2020-0116

DO - 10.1515/agms-2020-0116

M3 - Article

AN - SCOPUS:85099169121

SN - 2299-3274

VL - 8

SP - 305

EP - 334

JO - Analysis and Geometry in Metric Spaces

JF - Analysis and Geometry in Metric Spaces

IS - 1

ER -

Commutators on weighted Morrey spaces on spaces of homogeneous type

Abstract

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Harmonic analysis and dispersive partial differential equations

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Commutators on weighted Morrey spaces on spaces of homogeneous type

Abstract

Bibliographical note

Keywords

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Harmonic analysis and dispersive partial differential equations

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