A note on the Schrodinger maximal function
Number Theory
2016-09-20 v1
Authors:
Jean Bourgain
Abstract
It is shown that control of the Schrodinger maximal functions sup0<t<1∣eitΔf∣ for f∈Hs(Rn) requires s≥2(n+1)n
Keywords
Cite
@article{arxiv.1609.05744,
title = {A note on the Schrodinger maximal function},
author = {Jean Bourgain},
journal= {arXiv preprint arXiv:1609.05744},
year = {2016}
}
Comments
4 pages
Related papers
View all related →
Classical Analysis and ODEs · Mathematics
An Upbound of Hausdorff's Dimension of the Divergence Set of the fractional Schr\"odinger Operator on $H^s(\mathbb R^n)
Dan Li, Junfeng Li, Jie Xiao
2019-12-23
Classical Analysis and ODEs · Mathematics
A sharp Schrodinger maximal estimate in $\mathbb{R}^2$
Xiumin Du, Larry Guth, Xiaochun Li
2017-06-21
Classical Analysis and ODEs · Mathematics
Sharp $L^2$ estimate of Schr\"odinger maximal function in higher dimensions
Xiumin Du, Ruixiang Zhang
2019-03-14
Classical Analysis and ODEs · Mathematics
Pointwise convergence of sequential Schr\"odinger means
Chu-Hee Cho, Hyerim Ko, Youngwoo Koh, Sanghyuk Lee
2022-07-20
Analysis of PDEs · Mathematics
On the Schrodinger maximal function in higher dimension
Jean Bourgain
2012-01-17
Classical Analysis and ODEs · Mathematics
$L^p$-estimates of maximal function related to Schr\"{o}dinger Equation in $\mathbb{R}^2$
Xiumin Du, Xiaochun Li
2016-11-10
Classical Analysis and ODEs · Mathematics
On localization of the Schr\"odinger maximal operator
Shuanglin Shao
2010-06-15
Classical Analysis and ODEs · Mathematics
A Note on Non-tangential Convergence for Schr\"{o}dinger Operators
Wenjuan Li, Huiju Wang, Dunyan Yan
2021-06-18
Functional Analysis · Mathematics
Mapping properties of the Schr\"odinger maximal function on Damek--Ricci spaces
Utsav Dewan, Swagato K. Ray
2025-08-15
Classical Analysis and ODEs · Mathematics
The Maximal Function and Square Function Control the Variation: An Elementary Proof
Kevin Hughes, Ben Krause, Bartosz Trojan
2015-09-22
Functional Analysis · Mathematics
Restriction theorem for the Fourier-Hermite transform and solution of the Hermite-Schr\"odinger equation
Shyam Swarup Mondal, Jitendriya Swain
2022-03-08
Classical Analysis and ODEs · Mathematics
Pointwise convergence of Schr\"odinger solutions and multilinear refined Strichartz estimates
Xiumin Du, Larry Guth, Xiaochun Li, Ruixiang Zhang
2018-06-05
Combinatorics · Mathematics
Improved bounds for the Erd\H{o}s-Rogers function
W. T. Gowers, O. Janzer
2020-02-28
Classical Analysis and ODEs · Mathematics
Pointwise Convergence for sequences of Schr\"{o}dinger means in $\mathbb{R}^{2}$
Wenjuan Li, Huiju Wang, Dunyan Yan
2020-11-03
Classical Analysis and ODEs · Mathematics
On maximal functions for Mikhlin-Hoermander multipliers
Loukas Grafakos, Petr Honzik, Andreas Seeger
2010-03-15
Classical Analysis and ODEs · Mathematics
An improved necessary condition for the Schr\"odinger maximal estimate
Renato Lucà, Keith Rogers
2017-03-07
Analysis of PDEs · Mathematics
An improved maximal inequality for 2D fractional order Schr\"{o}dinger operators
Changxing Miao, Jianwei Yang, Jiqiang Zheng
2016-02-08
Probability · Mathematics
Restrictions of H\"older continuous functions
Omer Angel, Richárd Balka, András Máthé, Yuval Peres
2016-11-29
Classical Analysis and ODEs · Mathematics
On absolute convergence of Fourier integrals
E. Liflyand, R. Trigub
2009-06-01
Classical Analysis and ODEs · Mathematics
Maximal functions associated with families of homogeneous curves: $L^p$ bounds for $p\le 2$
Shaoming Guo, Joris Roos, Andreas Seeger, Po-Lam Yung
2020-04-17
Analysis of PDEs · Mathematics
Maximal regularity for time-fractional Schr\"odinger equations and application to nonlinear equations
S. E. Chorfi, F. Et-tahri, L. Maniar, M. Yamamoto
2026-03-18
Classical Analysis and ODEs · Mathematics
Pointwise convergence of solutions to Schr\"odinger equations
Sanghyuk Lee
2012-12-06
Optimization and Control · Mathematics
Control in the coefficients of an elliptic differential operator: topological derivatives and Pontryagin maximum principle
Daniel Wachsmuth
2024-08-01
Functional Analysis · Mathematics
Spherical maximal operators on radial functions
Andreas Seeger, Stephen Wainger, James Wright
2016-09-06
Number Theory · Mathematics
A modest improvement on the function $S(T)$
Timothy Trudgian
2013-10-10