Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A Marcinkiewicz maximal-multiplier theorem

Author: Richard Oberlin
Journal: Proc. Amer. Math. Soc. 141 (2013), 2081-2083
MSC (2010): Primary 42A45; Secondary 42A20
Published electronically: January 17, 2013
MathSciNet review: 3034433
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: For $ r < 2$, we prove the boundedness of a maximal operator formed by applying all multipliers $ m$ with $ \Vert m\Vert _{V^r} \leq 1$ to a given function.

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

  • 1. Michael Christ, Loukas Grafakos, Petr Honzík, and Andreas Seeger, Maximal functions associated with Fourier multipliers of Mikhlin-Hörmander type, Math. Z. 249 (2005), no. 1, 223-240. MR 2106977 (2005h:42024)
  • 2. Ronald Coifman, José Luis Rubio de Francia, and Stephen Semmes, Multiplicateurs de Fourier de $ L^p({\bf R})$ et estimations quadratiques, C. R. Acad. Sci. Paris Sér. I Math. 306 (1988), no. 8, 351-354. MR 934617 (89e:42009)
  • 3. Ciprian Demeter, Michael T. Lacey, Terence Tao, and Christoph Thiele, Breaking the duality in the return times theorem, Duke Math. J. 143 (2008), no. 2, 281-355. MR 2420509
  • 4. Michael T. Lacey, personal communication.
  • 5. -, Issues related to Rubio de Francia's Littlewood-Paley inequality, NYJM Monographs, vol. 2, State University of New York, University at Albany, Albany, NY, 2007. MR 2293255 (2007k:42048)
  • 6. Richard Oberlin, Andreas Seeger, Terence Tao, Christoph Thiele, and James Wright, A variation norm Carleson theorem, J. Eur. Math. Soc. 14 (2012), no. 2, 421-464. MR 2881301
  • 7. José L. Rubio de Francia, A Littlewood-Paley inequality for arbitrary intervals, Rev. Mat. Iberoamericana 1 (1985), no. 2, 1-14. MR 850681 (87j:42057)
  • 8. Terence Tao and James Wright, Endpoint multiplier theorems of Marcinkiewicz type, Rev. Mat. Iberoamericana 17 (2001), no. 3, 521-558. MR 1900894 (2003e:42014)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 42A45, 42A20

Retrieve articles in all journals with MSC (2010): 42A45, 42A20

Additional Information

Richard Oberlin
Affiliation: Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803-4918

Received by editor(s): October 4, 2011
Published electronically: January 17, 2013
Additional Notes: The author is supported in part by NSF Grant DMS-1068523.
Communicated by: Michael T. Lacey
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society