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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
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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.

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 $(1,1)$, 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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