Improved bounds for Stein's square functions

Sanghyuk Lee, Keith M. Rogers, Andreas Seeger

Type: Article

Publication Date: 2012-02-05

Citations: 48

DOI: https://doi.org/10.1112/plms/pdr067

Abstract

We prove a weighted norm inequality for the maximal Bochner–Riesz operator and the associated square-function. This yields new Lp(ℝd) bounds on classes of radial Fourier multipliers, for p⩾2+4/d with d⩾2, as well as space–time regularity results for the wave and Schrödinger equations.

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DIGITAL.CSIC (Spanish National Research Council (CSIC)) - View - PDF
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Works Cited by This (42)

Action	Title	Year	Authors
+	Radial Fourier Multipliers and Associated Maximal Functions	1985	Anthony Carbery
+	A note on Bochner-Riesz operators	1979	Antonio Cordóba
+ PDF Chat	Endpoint inequalities for Bochner-Riesz multipliers in the plane	1996	Andreas Seeger
+	On some singular Fourier multipliers	1981	Akihiko Miyachi
+	Weighted Norm Inequalities and Related Topics	1985	José Garcı́a-Cuerva J.-L. Rubio de Francia
+	Introduction to Fourier Analysis on Euclidean Spaces.	1971	Elias M. Stein Guido Weiss
+	Bilinear restriction estimates for surfaces with curvatures of different signs	2005	Sanghyuk Lee
+	A sharp bilinear restriction estimate for paraboloids	2002	Terence Tao
+ PDF Chat	Weighted inequalities for Bochner-Riesz means in the plane	2000	Anthony Carbery
+ PDF Chat	Estimates for some square functions of Littlewood-Paley type	1983	J.-L. Rubio de Francia