Counterexamples for multi-parameter weighted paraproducts
We build the plethora of counterexamples to bi-parameter two weight embedding theorems. Two weight one parameter embedding results (which is the same as results of boundedness of two weight classical paraproducts, or two weight Carleson embedding theorems) are well known since the works of Sawyer in...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Académie des sciences
2020-09-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.52/ |
| _version_ | 1797651530088710144 |
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| author | Mozolyako, Pavel Psaromiligkos, Georgios Volberg, Alexander |
| author_facet | Mozolyako, Pavel Psaromiligkos, Georgios Volberg, Alexander |
| author_sort | Mozolyako, Pavel |
| collection | DOAJ |
| description | We build the plethora of counterexamples to bi-parameter two weight embedding theorems. Two weight one parameter embedding results (which is the same as results of boundedness of two weight classical paraproducts, or two weight Carleson embedding theorems) are well known since the works of Sawyer in the 80’s. Bi-parameter case was considered by S. Y. A. Chang and R. Fefferman but only when underlying measure is Lebesgue measure. The embedding of holomorphic functions on bi-disc requires general input measure. In [9] we classified such embeddings if the output measure has tensor structure. In this note we give examples that without tensor structure requirement all results break down. |
| first_indexed | 2024-03-11T16:17:08Z |
| format | Article |
| id | doaj.art-3dbddfe8442940728d1f1084a777aae1 |
| institution | Directory Open Access Journal |
| issn | 1778-3569 |
| language | English |
| last_indexed | 2024-03-11T16:17:08Z |
| publishDate | 2020-09-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj.art-3dbddfe8442940728d1f1084a777aae12023-10-24T14:18:59ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692020-09-01358552953410.5802/crmath.5210.5802/crmath.52Counterexamples for multi-parameter weighted paraproductsMozolyako, Pavel0Psaromiligkos, Georgios1Volberg, Alexander2Department of Mathematics, Michigan State University, East Lansing, MI 48824, USADepartment of Mathematics, Michigan State University, East Lansing, MI 48824, USADepartment of Mathematics, Michigan State University, East Lansing, MI 48824, USAWe build the plethora of counterexamples to bi-parameter two weight embedding theorems. Two weight one parameter embedding results (which is the same as results of boundedness of two weight classical paraproducts, or two weight Carleson embedding theorems) are well known since the works of Sawyer in the 80’s. Bi-parameter case was considered by S. Y. A. Chang and R. Fefferman but only when underlying measure is Lebesgue measure. The embedding of holomorphic functions on bi-disc requires general input measure. In [9] we classified such embeddings if the output measure has tensor structure. In this note we give examples that without tensor structure requirement all results break down.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.52/ |
| spellingShingle | Mozolyako, Pavel Psaromiligkos, Georgios Volberg, Alexander Counterexamples for multi-parameter weighted paraproducts Comptes Rendus. Mathématique |
| title | Counterexamples for multi-parameter weighted paraproducts |
| title_full | Counterexamples for multi-parameter weighted paraproducts |
| title_fullStr | Counterexamples for multi-parameter weighted paraproducts |
| title_full_unstemmed | Counterexamples for multi-parameter weighted paraproducts |
| title_short | Counterexamples for multi-parameter weighted paraproducts |
| title_sort | counterexamples for multi parameter weighted paraproducts |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.52/ |
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