A COMPACT EXTENSION OF JOURNÉ’S T1 THEOREM ON PRODUCT SPACES

Mingming Cao; Kôzô Yabuta; Dachun Yang

doi:10.1090/tran/9206

A COMPACT EXTENSION OF JOURNÉ’S T1 THEOREM ON PRODUCT SPACES

Mingming Cao
, Kôzô Yabuta
, Dachun Yang

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

1 Scopus citations

Abstract

We prove a compact version of the T1 theorem for bi-parameter singular integrals. That is, if a bi-parameter singular integral operator T admits the compact full and partial kernel representations, and satisfies the weak compactness property, the diagonal CMO condition, and the product CMO condition, then T can be extended to a compact operator on L^p(w) for all 1 < p < ∞ and w ∈ Ap(ℝⁿ₁ × ℝⁿ₂). Even in the unweighted setting, it is the first time to give a compact extension of Journé’s T1 theorem on product spaces.

Original language	English
Pages (from-to)	6251-6309
Number of pages	59
Journal	Transactions of the American Mathematical Society
Volume	377
Issue number	9
DOIs	https://doi.org/10.1090/tran/9206
State	Published - Sep 2024
Externally published	Yes

Keywords

Bi-parameter singular integrals
Dyadic analysis
T1 theorem
compactness

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10.1090/tran/9206

Cite this

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title = "A COMPACT EXTENSION OF JOURN{\'E}{\textquoteright}S T1 THEOREM ON PRODUCT SPACES",

abstract = "We prove a compact version of the T1 theorem for bi-parameter singular integrals. That is, if a bi-parameter singular integral operator T admits the compact full and partial kernel representations, and satisfies the weak compactness property, the diagonal CMO condition, and the product CMO condition, then T can be extended to a compact operator on Lp(w) for all 1 < p < ∞ and w ∈ Ap(ℝn1 × ℝn2). Even in the unweighted setting, it is the first time to give a compact extension of Journ{\'e}{\textquoteright}s T1 theorem on product spaces.",

keywords = "Bi-parameter singular integrals, Dyadic analysis, T1 theorem, compactness",

author = "Mingming Cao and K{\^o}z{\^o} Yabuta and Dachun Yang",

note = "Publisher Copyright: {\textcopyright} 2024 American Mathematical Society.",

year = "2024",

month = sep,

doi = "10.1090/tran/9206",

language = "英语",

volume = "377",

pages = "6251--6309",

journal = "Transactions of the American Mathematical Society",

issn = "0002-9947",

publisher = "American Mathematical Society",

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T1 - A COMPACT EXTENSION OF JOURNÉ’S T1 THEOREM ON PRODUCT SPACES

AU - Cao, Mingming

AU - Yabuta, Kôzô

AU - Yang, Dachun

PY - 2024/9

Y1 - 2024/9

N2 - We prove a compact version of the T1 theorem for bi-parameter singular integrals. That is, if a bi-parameter singular integral operator T admits the compact full and partial kernel representations, and satisfies the weak compactness property, the diagonal CMO condition, and the product CMO condition, then T can be extended to a compact operator on Lp(w) for all 1 < p < ∞ and w ∈ Ap(ℝn1 × ℝn2). Even in the unweighted setting, it is the first time to give a compact extension of Journé’s T1 theorem on product spaces.

AB - We prove a compact version of the T1 theorem for bi-parameter singular integrals. That is, if a bi-parameter singular integral operator T admits the compact full and partial kernel representations, and satisfies the weak compactness property, the diagonal CMO condition, and the product CMO condition, then T can be extended to a compact operator on Lp(w) for all 1 < p < ∞ and w ∈ Ap(ℝn1 × ℝn2). Even in the unweighted setting, it is the first time to give a compact extension of Journé’s T1 theorem on product spaces.

KW - Bi-parameter singular integrals

KW - Dyadic analysis

KW - T1 theorem

KW - compactness

UR - https://www.scopus.com/pages/publications/85202027790

U2 - 10.1090/tran/9206

DO - 10.1090/tran/9206

M3 - 文章

AN - SCOPUS:85202027790

SN - 0002-9947

VL - 377

SP - 6251

EP - 6309

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 9

ER -

A COMPACT EXTENSION OF JOURNÉ’S T1 THEOREM ON PRODUCT SPACES

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Keywords

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