Sparse bounds for the discrete spherical maximal functions
Copyright policy )Sparse bounds for the discrete spherical maximal functions
We prove sparse bounds for the spherical maximal operator of Magyar, Stein and Wainger. The bounds are conjecturally sharp, and contain an endpoint estimate. The new method of proof is inspired by ones by Bourgain and Ionescu, is very efficient, and has not been used in the proof of sparse bounds before. The Hardy-Littlewood Circle method is used to decompose the multiplier into major and minor arc components. The efficiency arises as one only needs a single estimate on each element of the decomposition.
20 pages. A much stronger result in latest version. To appear in Pure and Applied Analysis
- Georgia Institute of Technology United States
- University of Costa Rica Costa Rica
- Mississippi School for Mathematics and Science United States
Spherical average, 11K70, Mathematics - Number Theory, Maximal functions, Littlewood-Paley theory, Harmonic analysis and almost periodicity in probabilistic number theory, spherical averages, sparse bounds, spherical maximal function, Mathematics - Classical Analysis and ODEs, Discrete, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Sparse, discrete, Number Theory (math.NT), 42B25
Spherical average, 11K70, Mathematics - Number Theory, Maximal functions, Littlewood-Paley theory, Harmonic analysis and almost periodicity in probabilistic number theory, spherical averages, sparse bounds, spherical maximal function, Mathematics - Classical Analysis and ODEs, Discrete, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Sparse, discrete, Number Theory (math.NT), 42B25
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).10 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Top 10%
Citations provided by BIP!Popularity provided by BIP!