Maximal function estimates of solutions to general dispersive partial differential equations期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Maximal function estimates of solutions to general dispersive partial differential equations

Authors:	Hans P. Heinig Sichun Wang

Affiliation:	Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, L8S 4K1, Canada ; Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, L8S 4K1, Canada

Abstract:	Let be the solution of the general dispersive initial value problem: $begin{displaymath}partial _tu-iOmega(D)u=0, quad u(x,0)=f(x), qquad (x,t)in mathbb{R}^n times mathbb{R}end{displaymath}$ and $S^{}_Omega f$ the global maximal operator of . Sharp weighted -esimates for $S^{}_Omega f$ with $fin H_s(mathbb{R}^n)$ are given for general phase functions .

Keywords:	Dispersive PDE, free Schr" odinger equation, phase functions, polynomials of principal type, regular zeroes, weighted $L^p$-spaces, Sobolev spaces

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