The multiplier problem for the polygon
The multiplier problem for the polygon
复制标题
多边形的乘数问题
DOI：
10.2307/1970926
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发表时间：
1977
影响因子：
4.9
通讯作者：
A. Córdoba
中科院分区：
文献类型：
--
作者：
A. Córdoba
我们用P表示R2中有N条边的多边形并考虑由Tf(e) = Xp(a)f(e)定义的算子，其中Xp是P的特征函数f表示f的傅里叶变换；很早以前我们就知道T是L ‘ ‘ （R2）上的有界算子，对于4/(3 + 2a)和4/(1 - 2a)之间的每一个p， T是L ’ ’ （R2）上的有界算子。多边形问题（出现在C. Fefferman的工作中，作为理解Bochner-Riesz乘法器Sa行为的自然步骤）要求对算子T的范数进行精确估计。与算子T相关的最大函数M定义为
Let us denote by P a polygon of N sides in R2 and consider the operator defined by Tf(e) = Xp(A)f(e), where Xp is the characteristic function of P and f denotes the Fourier transform of f; it has been known for a long time that T is a bounded operator on L"(R2), 1 a > 0, is bounded on L"(R2) for every p between 4/(3 + 2a) and 4/(1 - 2a). The polygon problem (which appears in the work of C. Fefferman as a natural step toward the understanding of the behavior of the Bochner-Riesz multipliers Sa) asks for sharp estimates for the norm of the operator T. Associated to the operator T there is a maximal function M defined by