ESTIMATES FOR RADIAL SOLUTIONS TO THE WAVE EQUATION

被引：4

作者：

Duoandikoetxea, Javier ^{[1
]}

Moyua, Adela ^{[1
]}

Oruetxebarria, Osane ^{[1
]}

机构：

[1] Univ Basque Country, Euskal Herriko Unibertsitatea, Dept Matemat, Apartado 644, E-48080 Bilbao, Spain

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2016年 / 144卷 / 04期

关键词：

Wave equation; radial solutions; weighted inequalities; SINGULAR-INTEGRALS; POWER WEIGHTS;

D O I：

10.1090/proc/12767

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the Cauchy problem for the wave equation with null initial position and radial initial velocity psi. With the solution u of this problem we define the operator S(psi) = sup(t>0) t(-1) vertical bar u(x, t)vertical bar. Using simple one-dimensional operators to bound pointwise the operator S we obtain weighted L-p estimates with power weights. Even for the unweighted estimates the result for dimension higher than 3 differs from the one with general functions.

引用

页码：1543 / 1552

页数：10

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