Geodesic
Improved $\ell^p$-Boundedness for Integral $k$-Spherical Maximal Functions
Discrete analysis (2018) Cet article a éte moissonné depuis la source Scholastica

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We improve the range of $\ell^p(\mathbb Z^d)$-boundedness of the integral $k$-spherical maximal functions introduced by Magyar. The previously best known bounds for the full $k$-spherical maximal function require the dimension $d$ to grow at least cubicly with the degree $k$. Combining ideas from our prior work with recent advances in the theory of Weyl sums by Bourgain, Demeter, and Guth and by Wooley, we reduce this cubic bound to a quadratic one. As an application, we deduce improved bounds in the ergodic Waring--Goldbach problem.
Publié le : 
@article{DAS_2018_a11,
     author = {Theresa C. Anderson and Brian Cook and Kevin Hughes and Angel Kumchev},
     title = {Improved $\ell^p${-Boundedness} for {Integral} $k${-Spherical} {Maximal} {Functions}},
     journal = {Discrete analysis},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DAS_2018_a11/}
}
TY  - JOUR
AU  - Theresa C. Anderson
AU  - Brian Cook
AU  - Kevin Hughes
AU  - Angel Kumchev
TI  - Improved $\ell^p$-Boundedness for Integral $k$-Spherical Maximal Functions
JO  - Discrete analysis
PY  - 2018
UR  - http://geodesic.mathdoc.fr/item/DAS_2018_a11/
LA  - en
ID  - DAS_2018_a11
ER  - 
%0 Journal Article
%A Theresa C. Anderson
%A Brian Cook
%A Kevin Hughes
%A Angel Kumchev
%T Improved $\ell^p$-Boundedness for Integral $k$-Spherical Maximal Functions
%J Discrete analysis
%D 2018
%U http://geodesic.mathdoc.fr/item/DAS_2018_a11/
%G en
%F DAS_2018_a11
Theresa C. Anderson; Brian Cook; Kevin Hughes; Angel Kumchev. Improved $\ell^p$-Boundedness for Integral $k$-Spherical Maximal Functions. Discrete analysis (2018). http://geodesic.mathdoc.fr/item/DAS_2018_a11/