Global <ImageObject Color="BlackWhite" FileRef="13660_2015_722_Article_IEq1.gif" Format="GIF" Rendition="HTML" Type="Linedraw"/> L 2 $L^{2}$ estimates for a class of maximal operators associated to general dispersive equations
 作者： Yong Ding,  Yaoming Niu 作者单位： 1School of Mathematical Sciences, Beijing Normal University2Faculty of Mathematics, Baotou Teachers College of Inner Mongolia University of Science and Technology 刊名： Journal of Inequalities and Applications, 2015, Vol.2015 (1), pp.1-20 来源数据库： Springer Nature Journal DOI： 10.1186/s13660-015-0722-4 关键词： dispersive equation;  maximal operator;  global L 2 $L^{2}$ estimate;  radial function; 原始语种摘要： Abstract(#br)For a function ϕ satisfying some suitable growth conditions, consider the general dispersive equation defined by { i ∂ t u + ϕ ( − Δ ) u = 0 , ( x , t ) ∈ R n × R , u ( x , 0 ) = f ( x ) , f ∈ S ( R n ) . $\bigl\{ \scriptsize{ \begin{array}{l} i\partial_{t}u+\phi(\sqrt{-\Delta})u=0,\quad (x,t)\in\mathbb {R}^{n}\times\mathbb{R}, \\ u(x,0)=f(x), \quad f\in\mathcal{S}(\mathbb{R}^{n}). \end{array} }\bigr.$ (∗) In the present paper, we give some global L 2 $L^{2}$ estimate for the maximal operator... S ϕ ∗ $S_{\phi}^{*}$ , which is defined by S ϕ ∗ f ( x ) = sup 0 < t < 1 | S t , ϕ f ( x ) | $S^{\ast}_{\phi}f(x)= \sup_{0< t<1} |S_{t,\phi}f(x)|$ , x ∈ R n $x\in\mathbb{R}^{n}$ , where S t , ϕ f $S_{t,\phi}f$ is a formal solution of the equation (∗). Especially, the estimates obtained in this paper can be applied to discuss the properties of solutions of the fractional Schrödinger equation, the fourth-order Schrödinger equation and the beam equation.

• 铅字　Guy In Front
• 　相关的
• operators　操作符
• maximal　最大的
• GIF　Guy In Front
• Type　Guy In Front
• estimates　估值
• dispersive　扩散的
• HTML　超文本置标语言
• general　普遍的
• associated　相关的
• class　相关的