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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 versus weak type


Authors: Loukas Grafakos and Mieczyslaw Mastylo
Journal: Proc. Amer. Math. Soc. 133 (2005), 1075-1081
MSC (2000): Primary 46B70, 42B99
Published electronically: November 1, 2004
MathSciNet review: 2117208
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Abstract: We prove that translation invariant multilinear operators of restricted weak type $(1,1,\dots , 1,q)$ must necessarily be of weak type $(1,1,\dots, 1,q)$. We give applications.


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Additional Information

Loukas Grafakos
Affiliation: Department of Mathematics, University of Missouri, Columbia, Missouri 65211
Email: loukas@math.missouri.edu

Mieczyslaw Mastylo
Affiliation: Faculty of Mathematics and Computer Science, A. Mickiewicz University – and – Institute of Mathematics, Polish Academy of Science (Poznań branch), Umultowska 87, 61-614 Poznań, Poland
Email: mastylo@amu.edu.pl

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07791-3
PII: S 0002-9939(04)07791-3
Keywords: Multilinear interpolation, restricted weak type estimates
Received by editor(s): November 6, 2003
Published electronically: November 1, 2004
Additional Notes: The first author was supported by the National Science Foundation under grant DMS 0099881.
The second author was supported by KBN Grant 1 P03A 013 26
Communicated by: Andreas Seeger
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.