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http://dx.doi.org/10.4134/BKMS.b170115

GLOBAL MAXIMAL ESTIMATE TO SOME OSCILLATORY INTEGRALS  

Niu, Yaoming (Faculty of Mathematics Baotou Teachers' College of Inner Mongolia University of Science and Technology)
Xue, Ying (Faculty of Mathematics Baotou Teachers' College of Inner Mongolia University of Science and Technology)
Publication Information
Bulletin of the Korean Mathematical Society / v.55, no.2, 2018 , pp. 533-543 More about this Journal
Abstract
Under the symbol ${\Omega}$ is a combination of ${\phi}_i$ ($i=1,2,3,{\ldots},n$) which has a suitable growth condition, for dimension n = 2 and $n{\geq}3$, when the initial data f belongs to homogeneous Sobolev space, we obtain the global $L^q$ estimate for maximal operators generated by operators family $\{S_{t,{\Omega}}\}_{t{\in}{\mathbb{R}}}$ associated with solution to dispersive equations, which extend some results in [27].
Keywords
nonelliptic $Schr{\ddot{o}}dinger$ equation; maximal operator; global estimate;
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