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Global maximal estimate to some oscillatory integrals

Yaoming Niu|Ying Xue
대한수학회 (The Korean Mathematical Society)|2018.03|대한수학회보 (Bulletin of the KMS)|제55권 제2호|pp. 533-543

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참고문헌

키워드

maximal operatornonelliptic Schr\"{o}dinger equationglobal estimate
주제분류수학

초록

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}.

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 $n\geq3,$ 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}.

참고문헌 (32)

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