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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 | References | Similar Articles | Additional Information

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 $(1,1)$.

References [Enhancements On Off] (What's this?)

  • 1. M. Akcoglu, J. Baxter, A. Bellow, and R. L. Jones, On restricted weak type $(1,1)$; the discrete case, Israel J. Math. 124 (2001), 285-297. MR 2002g:47060
  • 2. J. Brown, Ergodic Theory and Topological Dynamics, Academic Press, New York, 1976. MR 58:11323
  • 3. A. P. Calderón, Ergodic theory and translation invariant operators, Proc. Nat. Acad. Sci. U.S.A. 59 (1968), 349-353. MR 37:2939
  • 4. R. A. Fefferman, A theory of entropy in Fourier analysis, Adv. in Math. 30 (1978), 171-201.MR 81g:42022
  • 5. K. H. Moon, On restricted weak type $(1,1)$, Proc. Amer. Math. Soc. 42 (1974), 148-152.MR 49:5946
  • 6. E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press, Princeton, NJ, 1971. MR 46:4102
  • 7. S. Yano, An extrapolation theorem, J. Math. Soc. Japan 3 (1951), 296-305. MR 14:41c

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Additional Information

Paul A. Hagelstein
Affiliation: Department of Mathematics, Baylor University, Waco, Texas 76798

Roger L. Jones
Affiliation: Department of Mathematics, DePaul University, Chicago, Illinois 60614

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

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