Bulletin of the
Korean Mathematical Society BKMS

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