Bloom Type Upper Bounds in the Product BMO Setting
(2020) In Journal of Geometric Analysis 30(3). p.3181-3203- Abstract
We prove some Bloom type estimates in the product BMO setting. More specifically, for a bounded singular integral Tn in R n and a bounded singular integral T m in R m we prove that ‖[Tn1,[b,Tm2]]‖Lp(μ)→Lp(λ)≲[μ]Ap,[λ]Ap‖b‖BMOprod(ν),where p∈ (1 , ∞)... (More)
We prove some Bloom type estimates in the product BMO setting. More specifically, for a bounded singular integral Tn in R n and a bounded singular integral T m in R m we prove that ‖[Tn1,[b,Tm2]]‖Lp(μ)→Lp(λ)≲[μ]Ap,[λ]Ap‖b‖BMOprod(ν),where p∈ (1 , ∞) , μ, λ∈ A p and ν: = μ 1 / p λ - 1 / p is the Bloom weight. Here Tn1 is T n acting on the first variable, Tm2 is T m acting on the second variable, A p stands for the bi-parameter weights of R n × R m and BMO prod (ν) is a weighted product BMO space.
(Less)
- author
- Li, Kangwei ; Martikainen, Henri and Vuorinen, Emil LU
- organization
- publishing date
- 2020-07
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Bloom’s inequality, Iterated commutators, Product BMO, Weighted BMO
- in
- Journal of Geometric Analysis
- volume
- 30
- issue
- 3
- pages
- 23 pages
- publisher
- Springer
- external identifiers
-
- scopus:85064691623
- ISSN
- 1050-6926
- DOI
- 10.1007/s12220-019-00194-3
- language
- English
- LU publication?
- yes
- id
- 4f26e9b2-40a5-461a-a57e-5191461f370c
- date added to LUP
- 2019-05-07 11:10:54
- date last changed
- 2022-04-25 23:01:57
@article{4f26e9b2-40a5-461a-a57e-5191461f370c,
abstract = {{<p> We prove some Bloom type estimates in the product BMO setting. More specifically, for a bounded singular integral T<sub>n</sub> in R <sup>n</sup> and a bounded singular integral T <sub>m</sub> in R <sup>m</sup> we prove that ‖[Tn1,[b,Tm2]]‖Lp(μ)→Lp(λ)≲[μ]Ap,[λ]Ap‖b‖BMOprod(ν),where p∈ (1 , ∞) , μ, λ∈ A <sub>p</sub> and ν: = μ <sup>1</sup> <sup>/</sup> <sup>p</sup> λ <sup>-</sup> <sup>1</sup> <sup>/</sup> <sup>p</sup> is the Bloom weight. Here Tn1 is T <sub>n</sub> acting on the first variable, Tm2 is T <sub>m</sub> acting on the second variable, A <sub>p</sub> stands for the bi-parameter weights of R <sup>n</sup> × R <sup>m</sup> and BMO <sub>prod</sub> (ν) is a weighted product BMO space. </p>}},
author = {{Li, Kangwei and Martikainen, Henri and Vuorinen, Emil}},
issn = {{1050-6926}},
keywords = {{Bloom’s inequality; Iterated commutators; Product BMO; Weighted BMO}},
language = {{eng}},
number = {{3}},
pages = {{3181--3203}},
publisher = {{Springer}},
series = {{Journal of Geometric Analysis}},
title = {{Bloom Type Upper Bounds in the Product BMO Setting}},
url = {{http://dx.doi.org/10.1007/s12220-019-00194-3}},
doi = {{10.1007/s12220-019-00194-3}},
volume = {{30}},
year = {{2020}},
}