Restricted weak type on maximal linear and multilinear integral maps
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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.References
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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
- 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
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 1343-1353
- MSC (2000): Primary 42B35, 46B70, 42B99
- DOI: https://doi.org/10.1090/S0002-9939-06-08798-3
- MathSciNet review: 2276643