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Restricted weak type versus weak type
Author(s):
Loukas
Grafakos;
Mieczyslaw
Mastylo
Journal:
Proc. Amer. Math. Soc.
133
(2005),
1075-1081.
MSC (2000):
Primary 46B70, 42B99
Posted:
November 1, 2004
MathSciNet review:
2117208
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Abstract:
We prove that translation invariant multilinear operators of restricted weak type  must necessarily be of weak type  . We give applications.
References:
-
- [BG]
- D. Bilyk and L. Grafakos, Interplay between distributional estimates and boundedness of operators, submitted.
- [GT]
- L. Grafakos and R. Torres, Multilinear Calderón-Zygmund theory, Adv. in Math. 165 (2002), 124-164. MR 1880324 (2002j:42029)
- [M]
- K. H. Moon, On restricted weak type
 , Proc. Amer. Math. Soc. 42 (1974), 148-152. MR 0341196 (49:5946) - [SW]
- E. M. Stein and G. Weiss, An extension of a theorem of Marcinkiewicz and some of its applications, J. Math. Mech. 8 (1959), 263-284. MR 0107163 (21:5888)
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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 (Poznan branch), Umultowska 87, 61-614 Poznan, Poland
Email:
mastylo@amu.edu.pl
DOI:
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
Posted:
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
Copyright of article:
Copyright
2004,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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