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

 

On restricted weak type $(1,1)$: The continuous case


Authors: Paul A. Hagelstein and Roger L. Jones
Journal: Proc. Amer. Math. Soc. 133 (2005), 185-190
MSC (2000): Primary 42B35; Secondary 37A25
Published electronically: June 2, 2004
MathSciNet review: 2085168
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Abstract: Let $\mathbb{T} $ denote the unit circle. An example of a sublinear translation-invariant operator $T$ acting on $L^{1}\left(\mathbb{T}\right)$ is given such that $T$ is of restricted weak type $(1,1)$ but not of weak type $(1,1)$.


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Additional Information

Paul A. Hagelstein
Affiliation: Department of Mathematics, Baylor University, Waco, Texas 76798
Email: paul_hagelstein@baylor.edu

Roger L. Jones
Affiliation: Department of Mathematics, DePaul University, Chicago, Illinois 60614
Email: rjones@condor.depaul.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07530-6
PII: S 0002-9939(04)07530-6
Received by editor(s): April 14, 2003
Received by editor(s) in revised form: September 12, 2003
Published electronically: June 2, 2004
Additional Notes: The first author’s research was partially supported by the Baylor University Summer Sabbatical Program
The second author was partially supported by a research leave granted by DePaul University’s Research Council
Communicated by: Andreas Seeger
Article copyright: © Copyright 2004 American Mathematical Society