赫茨与费弗曼：对称与非对称的博赫纳-里斯理论
Herz versus Fefferman: Symmetric and asymmetric Bochner--Riesz theory
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中文总结 AI 辅助
该研究针对带不等维端点的非紧流形一维模型，刻画了其博赫纳-里斯可和性的L^p有界性，揭示了非对称情形下的额外限制及端点间相互作用的影响。
中文摘要 AI 辅助
我们研究带端点的非紧流形一维模型的博赫纳-里斯可和性，每个端点具有有效欧氏维数，且不同端点的维数可不同。核心是对称与非对称情形的对比：当端点维数一致时，该模型遵循欧氏拉普拉斯算子的赫茨径向理论；当端点维数不等时，会出现费弗曼型障碍，类似高维傅里叶分析中的球乘子障碍，即便模型本身是一维的。我们完整刻画了对应谱投影与博赫纳-里斯平均的L^p有界性，非对称情形下，有界性范围包含一个依赖端点维数差值的额外限制，该限制在赫茨径向模型中不存在，表明不等端点空间上的博赫纳-里斯可和性不仅受最大端点维数支配，还受端点间相互作用影响。
英文摘要
We study Bochner--Riesz summability for a one-dimensional model of noncompact manifolds with ends. Each end has an effective Euclidean dimension, and these dimensions may differ from one end to another. The central point is the contrast between the symmetric and asymmetric cases. When the end dimensions agree, the model follows Herz's radial theory for the Euclidean Laplacian. When they are unequal, a Fefferman-type obstruction appears, analogous to the ball multiplier obstruction in higher-dimensional Fourier analysis, even though the model itself is one-dimensional. We give a complete characterisation of the \(L^p\)-boundedness of the corresponding spectral projections and Bochner--Riesz means. In the asymmetric case, the boundedness range contains an additional restriction depending on the difference between the end dimensions. This restriction is absent from Herz's radial model and shows that Bochner--Riesz summability on spaces with unequal ends is governed not only by the maximal end dimension, but also by the interaction between the ends.
