Weighted inequalities for multivariable dyadic paraproducts

Using Wilson's Haar basis in Rn, which is different than the usual tensor product Haar functions, we define its associated dyadic paraproduct in Rn. We can then extend "trivially" Beznosova's Bellman function proof of the linear bound in L2(w) with respect to [w]A2 for the 1-dime...

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Detalhes bibliográficos
Autor: Chung, Daewon
Formato: artículo
Fecha de publicación:2011
País:España
Recursos:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:76165
Acesso em linha:https://ddd.uab.cat/record/76165
https://dx.doi.org/urn:doi:10.5565/PUBLMAT_55211_10
Access Level:acceso abierto
Palavra-chave:Operator-weighted inequalities
Multivariable dyadic paraproduct
Anisotropic Ap-weights
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spelling Weighted inequalities for multivariable dyadic paraproductsChung, DaewonOperator-weighted inequalitiesMultivariable dyadic paraproductAnisotropic Ap-weightsUsing Wilson's Haar basis in Rn, which is different than the usual tensor product Haar functions, we define its associated dyadic paraproduct in Rn. We can then extend "trivially" Beznosova's Bellman function proof of the linear bound in L2(w) with respect to [w]A2 for the 1-dimensional dyadic paraproduct. Here trivial means that each piece of the argument that had a Bellman function proof has an n-dimensional counterpart that holds with the same Bellman function. The lemma that allows for this painless extension we call the good Bellman function Lemma. Furthermore the argument allows to obtain dimensionless bounds in the anisotropic case. 22011-01-0120112011-01-01Articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/76165https://dx.doi.org/urn:doi:10.5565/PUBLMAT_55211_10reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengopen accesshttp://purl.org/coar/access_right/c_abf2Aquest material està protegit per drets d'autor i/o drets afins. Podeu utilitzar aquest material en funció del que permet la legislació de drets d'autor i drets afins d'aplicació al vostre cas. Per a d'altres usos heu d'obtenir permís del(s) titular(s) de drets.https://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:761652026-06-06T12:50:31Z
dc.title.none.fl_str_mv Weighted inequalities for multivariable dyadic paraproducts
title Weighted inequalities for multivariable dyadic paraproducts
spellingShingle Weighted inequalities for multivariable dyadic paraproducts
Chung, Daewon
Operator-weighted inequalities
Multivariable dyadic paraproduct
Anisotropic Ap-weights
title_short Weighted inequalities for multivariable dyadic paraproducts
title_full Weighted inequalities for multivariable dyadic paraproducts
title_fullStr Weighted inequalities for multivariable dyadic paraproducts
title_full_unstemmed Weighted inequalities for multivariable dyadic paraproducts
title_sort Weighted inequalities for multivariable dyadic paraproducts
dc.creator.none.fl_str_mv Chung, Daewon
author Chung, Daewon
author_facet Chung, Daewon
author_role author
dc.subject.none.fl_str_mv Operator-weighted inequalities
Multivariable dyadic paraproduct
Anisotropic Ap-weights
topic Operator-weighted inequalities
Multivariable dyadic paraproduct
Anisotropic Ap-weights
description Using Wilson's Haar basis in Rn, which is different than the usual tensor product Haar functions, we define its associated dyadic paraproduct in Rn. We can then extend "trivially" Beznosova's Bellman function proof of the linear bound in L2(w) with respect to [w]A2 for the 1-dimensional dyadic paraproduct. Here trivial means that each piece of the argument that had a Bellman function proof has an n-dimensional counterpart that holds with the same Bellman function. The lemma that allows for this painless extension we call the good Bellman function Lemma. Furthermore the argument allows to obtain dimensionless bounds in the anisotropic case.
publishDate 2011
dc.date.none.fl_str_mv 2
2011-01-01
2011
2011-01-01
dc.type.none.fl_str_mv Article
http://purl.org/coar/resource_type/c_6501
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https://dx.doi.org/urn:doi:10.5565/PUBLMAT_55211_10
url https://ddd.uab.cat/record/76165
https://dx.doi.org/urn:doi:10.5565/PUBLMAT_55211_10
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://rightsstatements.org/vocab/InC/1.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
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dc.source.none.fl_str_mv reponame:Dipòsit Digital de Documents de la UAB
instname:Universitat Autònoma de Barcelona
instname_str Universitat Autònoma de Barcelona
reponame_str Dipòsit Digital de Documents de la UAB
collection Dipòsit Digital de Documents de la UAB
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