A Marcinkiewicz maximal-multiplier theorem

Oberlin, Richard

doi:10.1090/S0002-9939-2013-11485-1

A Marcinkiewicz maximal-multiplier theorem
HTML articles powered by AMS MathViewer

by Richard Oberlin PDF

Proc. Amer. Math. Soc. 141 (2013), 2081-2083 Request permission

Abstract:

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

References

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, DOI 10.1007/s00209-004-0698-0
Ronald Coifman, José Luis Rubio de Francia, and Stephen Semmes, Multiplicateurs de Fourier de $L^p(\textbf {R})$ et estimations quadratiques, C. R. Acad. Sci. Paris Sér. I Math. 306 (1988), no. 8, 351–354 (French, with English summary). MR 934617
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, DOI 10.1215/00127094-2008-020
Michael T. Lacey, personal communication.
Michael T. Lacey, Issues related to Rubio de Francia’s Littlewood-Paley inequality, New York Journal of Mathematics. NYJM Monographs, vol. 2, State University of New York, University at Albany, Albany, NY, 2007. MR 2293255
Richard Oberlin, Andreas Seeger, Terence Tao, Christoph Thiele, and James Wright, A variation norm Carleson theorem, J. Eur. Math. Soc. (JEMS) 14 (2012), no. 2, 421–464. MR 2881301, DOI 10.4171/JEMS/307
José L. Rubio de Francia, A Littlewood-Paley inequality for arbitrary intervals, Rev. Mat. Iberoamericana 1 (1985), no. 2, 1–14. MR 850681, DOI 10.4171/RMI/7
Terence Tao and James Wright, Endpoint multiplier theorems of Marcinkiewicz type, Rev. Mat. Iberoamericana 17 (2001), no. 3, 521–558. MR 1900894, DOI 10.4171/RMI/303