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- 저자 : Yaoming Niu (검색결과 4 건)
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Estimates for Schr\"{o}dinger maximal operators along curve with complex time
Yaoming Niu,Ying Xue 대한수학회 2020 대한수학회지 Vol.57 No.1
In the present paper, we give some characterization of the $L^{2}$ maximal estimate for the operator $P_{a,\gamma}^{t}f\big(\Gamma(x,t)\big)$ along curve with complex time, which is defined by $$P_{a,\gamma}^{t}f\big(\Gamma(x,t)\big) =\int_{\mathbb{R}} e^{i\Gamma(x,t)\xi}e^{it|\xi|^{a}} e^{-t^{\gamma}|\xi|^{a}} \hat{f}(\xi)d\xi,$$ where $t,\gamma>0$ and $a\geq2,$ curve $\Gamma$ is a function such that $\Gamma:\mathbb{R}\times[0,1]\rightarrow\mathbb{R},$ and satisfies H\"{o}lder's condition of order $\sigma$ and bilipschitz conditions. The authors extend the results of the Schr\"{o}dinger type with complex time of Bailey \cite{Bailey} and Cho, Lee and Vargas \cite{CLV} to Schr\"{o}dinger operators along the curves.
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Global maximal estimate to some oscillatory integrals
Yaoming Niu,Ying Xue 대한수학회 2018 대한수학회보 Vol.55 No.2
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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ESTIMATES FOR SCHRÖDINGER MAXIMAL OPERATORSALONG CURVE WITH COMPLEX TIME
Niu, Yaoming,Xue, Ying Korean Mathematical Society 2020 대한수학회지 Vol.57 No.1
In the present paper, we give some characterization of the L<sub>2</sub> maximal estimate for the operator P<sup>t</sup><sub>a,γ</sub>f(Γ(x, t)) along curve with complex time, which is defined by $$P^t_{a,{\gamma}}f({\Gamma}(x,t))={\displaystyle\smashmargin{2}{\int\nolimits_{\mathbb{R}}}}\;e^{i{\Gamma}(x,t){\xi}}e^{it{\mid}{\xi}{\mid}^a}e^{-t^{\gamma}{\mid}{\xi}{\mid}^a}{\hat{f}}({\xi})d{\xi}$$, where t, γ > 0 and a ≥ 2, curve Γ is a function such that Γ : ℝ×[0, 1] → ℝ, and satisfies Hölder's condition of order σ and bilipschitz conditions. The authors extend the results of the Schrödinger type with complex time of Bailey [1] and Cho, Lee and Vargas [3] to Schrödinger operators along the curves.
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GLOBAL MAXIMAL ESTIMATE TO SOME OSCILLATORY INTEGRALS
Niu, Yaoming,Xue, Ying Korean Mathematical Society 2018 대한수학회보 Vol.55 No.2
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].
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