Estimates for multiparameter maximal operators of Schrodinger type

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:411

Article

Sjolin, Per¹  Soria, Fernando^2,3 

[1] Royal Inst Technol, Dept Math, S-10044 Stockholm, Sweden

[2] Univ Autonoma Madrid, Dept Matemat, E-28049 Madrid, Spain

[3] Univ Autonoma Madrid, Inst Ciencias Matemat CSIC UAM UCM UC3M, E-28049 Madrid, Spain

关键词: Maximal operator;    Schrodinger equation;    Oscillatory integrals;   

DOI  :  10.1016/j.jmaa.2013.09.037

来源: Elsevier

【 摘 要 】

Multiparameter maximal estimates are considered for operators of Schrodinger type. Sharp and almost sharp results, that extend work by Rogers and Villarroya, are obtained. We provide new estimates via the integrability of the kernel which naturally appears with a TT* argument and discuss the behavior at the endpoints. We treat in particular the case of global integrability of the maximal operator on finite time for solutions to the linear Schrodinger equation and make some comments on an open problem. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free