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.
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页码：1543 / 1552
页数：10
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