Vol. 11, No. 2, 2018

Download this article
Download this article For screen
For printing
Recent Issues

Volume 16
Issue 7, 1485–1744
Issue 6, 1289–1483
Issue 5, 1089–1288
Issue 4, 891–1088
Issue 3, 613–890
Issue 2, 309–612
Issue 1, 1–308

Volume 15, 8 issues

Volume 14, 8 issues

Volume 13, 8 issues

Volume 12, 8 issues

Volume 11, 8 issues

Volume 10, 8 issues

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Author Index
To Appear
 
Other MSP Journals
Radial Fourier multipliers in $\mathbb{R}^3$ and $\mathbb{R}^4$

Laura Cladek

Vol. 11 (2018), No. 2, 467–498
Abstract

We prove that for radial Fourier multipliers m : 3 supported compactly away from the origin, Tm is restricted strong type (p,p) if K = m̂ is in Lp(3), in the range 1 < p < 13 12. We also prove an Lp characterization for radial Fourier multipliers in four dimensions; namely, for radial Fourier multipliers m : 4 supported compactly away from the origin, Tm is bounded on Lp(4) if and only if K = m̂ is in Lp(4), in the range 1 < p < 36 29. Our method of proof relies on a geometric argument that exploits bounds on sizes of multiple intersections of 3-dimensional annuli to control numbers of tangencies between pairs of annuli in three and four dimensions.

Keywords
Fourier multipliers, radial functions, incidence geometry, local smoothing
Mathematical Subject Classification 2010
Primary: 42B15
Milestones
Received: 12 February 2017
Revised: 9 July 2017
Accepted: 10 August 2017
Published: 17 October 2017
Authors
Laura Cladek
Department of Mathematics
University of Wisconsin
Madison, WI
United States