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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Restricted weak type on maximal linear and multilinear integral maps


Author: Oscar Blasco
Journal: Proc. Amer. Math. Soc. 135 (2007), 1343-1353
MSC (2000): Primary 42B35, 46B70, 42B99
Published electronically: November 13, 2006
MathSciNet review: 2276643
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Abstract: It is shown that multilinear operators of the form $ T(f_1,...,f_k)(x)$ $ =\int_{\mathbb{R}^n}K(x,y_1,...,y_k)f_1(y_1)... f_k(y_k)dy_1...dy_k$ of restricted weak type $ (1,...,1,q)$ are always of weak type $ (1,...,1,q)$ whenever the map $ x\to K_x$ is a locally integrable $ L^1(\mathbb{R}^n)$-valued function.


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Additional Information

Oscar Blasco
Affiliation: Departamento de Análisis Matemático, Universidad de Valencia, 46100 Burjassot, Valencia, Spain
Email: Oscar.Blasco@uv.es

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08798-3
PII: S 0002-9939(06)08798-3
Keywords: Restricted weak type estimated, multilinear operators
Received by editor(s): November 21, 2005
Published electronically: November 13, 2006
Additional Notes: The author was supported by Spanish projects BFM2002-04013-C02-01 and MTM2005-8350-C03-03
Communicated by: Michael T. Lacey
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.