Bull. Korean Math. Soc. 2018; 55(2): 533-543
Online first article March 8, 2018 Printed March 1, 2018
https://doi.org/10.4134/BKMS.b170115
Copyright © The Korean Mathematical Society.
Yaoming Niu, Ying Xue
Baotou Teachers' College of Inner Mongolia University of Science and Technology, Baotou Teachers' College of Inner Mongolia University of Science and Technology
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 $n\geq3,$ 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 \cite{Sjolin8}.
Keywords: nonelliptic Schr\"{o}dinger equation, maximal operator, global estimate
MSC numbers: Primary 42B15; Secondary 42B25
2021; 58(2): 277-303
1999; 36(1): 25-31
2001; 38(1): 93-100
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd