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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}.
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참고문헌 (32)
참고문헌 신청
J. Bourgain / 2013 / On the Schrodinger maximal functionin higher dimension / Proc. Steklov Inst. Math. 280(1):46~60
J. Bourgain / 2016 / A note on the Schrodinger maximal function / J. Anal. Math. 130:393~396
A. Carbery / 1983 / Radial Fourier multipliers and associated maximal functions, in Recent progress in Fourier analysis;North-Holland Math. Stud., 111, Notas Mat., 101 / North-Holland :49~56
L. Carleson / Some analytic problems related to statistical mechanics, in Euclidean harmonic analysis / Proc. Sem. :5~45
Y. Cho / 2013 / Strichartz estimates in spherical coordinates / Indiana Univ. Math. J. 62(3):991~1020
J. Bourgain / 2016 / A note on the Schrodinger maximal function / J. Anal. Math. 130:393~396
A. Carbery / 1983 / Radial Fourier multipliers and associated maximal functions, in Recent progress in Fourier analysis;North-Holland Math. Stud., 111, Notas Mat., 101 / North-Holland :49~56
L. Carleson / Some analytic problems related to statistical mechanics, in Euclidean harmonic analysis / Proc. Sem. :5~45
Y. Cho / 2013 / Strichartz estimates in spherical coordinates / Indiana Univ. Math. J. 62(3):991~1020
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