Multilinear operator-valued calderón-zygmund theory
We develop a general theory of multilinear singular integrals with operator- valued kernels, acting on tuples of UMD Banach spaces. This, in particular, involves investigating multilinear variants of the R-boundedness condition naturally arising in operator-valued theory. We proceed by establishing...
| Authors: | ; ; ; |
|---|---|
| Format: | Article |
| Status: | Accepted version |
| Publication date: | 2020 |
| Country: | España |
| Institution: | Basque Center for Applied Mathematics (BCAM) |
| Repository: | BIRD. BCAM's Institutional Repository Data |
| OAI Identifier: | oai:bird.bcamath.org:20.500.11824/1213 |
| Online Access: | http://hdl.handle.net/20.500.11824/1213 https://doi.org/10.1016/j.jfa.2020.108666 |
| Access Level: | Open access |
| Keyword: | Calderón–Zygmund operators Operator-valued analysis Multilinear analysis UMD spaces |
| _version_ | 1878739049105063936 |
|---|---|
| author | Di Plinio, F. |
| author2 | Li, K. Martikainen, H. Vuorinen, E. |
| author2_role | author author author |
| author_browse | Di Plinio, F. Li, K. Martikainen, H. Vuorinen, E. |
| author_facet | Di Plinio, F. Li, K. Martikainen, H. Vuorinen, E. |
| author_role | author |
| collection | BIRD. BCAM's Institutional Repository Data |
| description | We develop a general theory of multilinear singular integrals with operator- valued kernels, acting on tuples of UMD Banach spaces. This, in particular, involves investigating multilinear variants of the R-boundedness condition naturally arising in operator-valued theory. We proceed by establishing a suitable representation of mul- tilinear, operator-valued singular integrals in terms of operator-valued dyadic shifts and paraproducts, and studying the boundedness of these model operators via dyadic- probabilistic Banach space-valued analysis. In the bilinear case, we obtain a T(1)-type theorem without any additional assumptions on the Banach spaces other than the nec- essary UMD. Higher degrees of multilinearity are tackled via a new formulation of the Rademacher maximal function (RMF) condition. In addition to the natural UMD lat- tice cases, our RMF condition covers suitable tuples of non-commutative Lp-spaces. We employ our operator-valued theory to obtain new multilinear, multi-parameter, operator- valued theorems in the natural setting of UMD spaces with property α. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | ES_ba25f736c7d8aeb1f22d8a265b1ca4f3 |
| institution | Basque Center for Applied Mathematics (BCAM) |
| instname_str | Basque Center for Applied Mathematics (BCAM) |
| network_acronym_str | ES |
| network_name_str | España |
| oai_identifier_str | oai:bird.bcamath.org:20.500.11824/1213 |
| publishDate | 2020 |
| publishDateSort | 2020 |
| reponame_str | BIRD. BCAM's Institutional Repository Data |
| spelling | Multilinear operator-valued calderón-zygmund theory Di Plinio, F. Li, K. Martikainen, H. Vuorinen, E. Calderón–Zygmund operators Operator-valued analysis Multilinear analysis UMD spaces We develop a general theory of multilinear singular integrals with operator- valued kernels, acting on tuples of UMD Banach spaces. This, in particular, involves investigating multilinear variants of the R-boundedness condition naturally arising in operator-valued theory. We proceed by establishing a suitable representation of mul- tilinear, operator-valued singular integrals in terms of operator-valued dyadic shifts and paraproducts, and studying the boundedness of these model operators via dyadic- probabilistic Banach space-valued analysis. In the bilinear case, we obtain a T(1)-type theorem without any additional assumptions on the Banach spaces other than the nec- essary UMD. Higher degrees of multilinearity are tackled via a new formulation of the Rademacher maximal function (RMF) condition. In addition to the natural UMD lat- tice cases, our RMF condition covers suitable tuples of non-commutative Lp-spaces. We employ our operator-valued theory to obtain new multilinear, multi-parameter, operator- valued theorems in the natural setting of UMD spaces with property α. http://hdl.handle.net/20.500.11824/1213 https://doi.org/10.1016/j.jfa.2020.108666 |
| spellingShingle | Multilinear operator-valued calderón-zygmund theory Di Plinio, F. Calderón–Zygmund operators Operator-valued analysis Multilinear analysis UMD spaces |
| status_str | acceptedVersion |
| title | Multilinear operator-valued calderón-zygmund theory |
| title_full | Multilinear operator-valued calderón-zygmund theory |
| title_fullStr | Multilinear operator-valued calderón-zygmund theory |
| title_full_unstemmed | Multilinear operator-valued calderón-zygmund theory |
| title_short | Multilinear operator-valued calderón-zygmund theory |
| title_sort | Multilinear operator-valued calderón-zygmund theory |
| topic | Calderón–Zygmund operators Operator-valued analysis Multilinear analysis UMD spaces |
| topic_facet | Calderón–Zygmund operators Operator-valued analysis Multilinear analysis UMD spaces |
| url | http://hdl.handle.net/20.500.11824/1213 https://doi.org/10.1016/j.jfa.2020.108666 |