New maximal functions and multiple weights for the multilinear Calderón–Zygmund theory
A multi(sub)linear maximal operator that acts on the product of m Lebesgue spaces and is smaller than the m-fold product of the Hardy–Littlewood maximal function is studied. The operator is used to obtain a precise control on multilinear singular integral operators of Calderón–Zygmund type and to bu...
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| Published in | Advances in mathematics (New York. 1965) Vol. 220; no. 4; pp. 1222 - 1264 |
|---|---|
| Main Authors | , , , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Inc
01.03.2009
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0001-8708 1090-2082 |
| DOI | 10.1016/j.aim.2008.10.014 |
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| Abstract | A multi(sub)linear maximal operator that acts on the product of
m Lebesgue spaces and is smaller than the
m-fold product of the Hardy–Littlewood maximal function is studied. The operator is used to obtain a precise control on multilinear singular integral operators of Calderón–Zygmund type and to build a theory of weights adapted to the multilinear setting. A natural variant of the operator which is useful to control certain commutators of multilinear Calderón–Zygmund operators with
BMO functions is then considered. The optimal range of strong type estimates, a sharp end-point estimate, and weighted norm inequalities involving both the classical Muckenhoupt weights and the new multilinear ones are also obtained for the commutators. |
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| AbstractList | A multi(sub)linear maximal operator that acts on the product of
m Lebesgue spaces and is smaller than the
m-fold product of the Hardy–Littlewood maximal function is studied. The operator is used to obtain a precise control on multilinear singular integral operators of Calderón–Zygmund type and to build a theory of weights adapted to the multilinear setting. A natural variant of the operator which is useful to control certain commutators of multilinear Calderón–Zygmund operators with
BMO functions is then considered. The optimal range of strong type estimates, a sharp end-point estimate, and weighted norm inequalities involving both the classical Muckenhoupt weights and the new multilinear ones are also obtained for the commutators. |
| Author | Lerner, Andrei K. Trujillo-González, Rodrigo Ombrosi, Sheldy Torres, Rodolfo H. Pérez, Carlos |
| Author_xml | – sequence: 1 givenname: Andrei K. surname: Lerner fullname: Lerner, Andrei K. email: aklerner@netvision.net.il organization: Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, 41080 Sevilla, Spain – sequence: 2 givenname: Sheldy surname: Ombrosi fullname: Ombrosi, Sheldy email: sombrosi@uns.edu.ar organization: Departamento de Matemática, Universidad Nacional del Sur, Bahía Blanca, 8000, Argentina – sequence: 3 givenname: Carlos surname: Pérez fullname: Pérez, Carlos email: carlosperez@us.es organization: Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, 41080 Sevilla, Spain – sequence: 4 givenname: Rodolfo H. surname: Torres fullname: Torres, Rodolfo H. email: torres@math.ku.edu organization: Department of Mathematics, University of Kansas, 405 Snow Hall 1460 Jayhawk Blvd, Lawrence, Kansas 66045-7523, USA – sequence: 5 givenname: Rodrigo surname: Trujillo-González fullname: Trujillo-González, Rodrigo email: rotrujil@ull.es organization: Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna, S.C. de Tenerife, Spain |
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