Circular average relative to fractal measures

Seheon Ham, Hyerim Ko, Sanghyuk Lee

Type: Article

Publication Date: 2022-01-01

Citations: 2

DOI: https://doi.org/10.3934/cpaa.2022100

Abstract

We prove new $L^p$- $L^q$ estimates for averages over dilates of the circle with respect to $\alpha$-dimensional fractal measure, which unify different types of maximal estimates for the circular average. Our results are consequences of $L^p$- $L^q$ smoothing estimates for the wave operator relative to fractal measures. We also discuss similar results concerning the spherical averages.

Locations

Communications on Pure &amp Applied Analysis - View - PDF
arXiv (Cornell University) - View - PDF
DataCite API - View

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Works Cited by This (36)

Action	Title	Year	Authors
+	Fourier Analysis and Hausdorff Dimension	2015	Pertti Mattila
+ PDF Chat	A generalization of Bourgain’s circular maximal theorem	1997	Wilhelm Schlag
+	Endpoint estimates for the circular maximal function	2002	Sanghyuk Lee
+ PDF Chat	On the Wolff circular maximal function	2012	Joshua Zahl
+ PDF Chat	Packing spheres and fractal Strichartz estimates in $\mathbb {R}^d$ for $d\geq 3$	2006	Daniel M. Oberlin
+	On a Problem Related to Sphere and Circle Packing	1999	Themis Mitsis
+	Averages in the plane over convex curves and maximal operators	1986	Jean Bourgain
+ PDF Chat	Radial Fourier multipliers in high dimensions	2011	Yaryong Heo Fëdor Nazarov Andreas Seeger
+	A Kakeya-type problem for circles	1997	Thomas Wolff
+	Maximal functions: Spherical means	1976	Elias M. Stein