论文标题
一类Bôchner-riesz内核的$ l^p $集成性的注释
A note on the $L^p$ integrability of a class of Bôchner-Riesz kernels
论文作者
论文摘要
对于一般的紧凑型$γ$的任意编纂，可以考虑Bôchner-riesz乘数的$ l^p $映射属性$$ m_ {γ，α}（ζ）\ = \ = \ {\ rm dist}（\ rm dist}（ζ）即使对于球体，$γ= {\ mathbb s}^{n-1} $，精确的$ l^p $界限范围仍然是欧几里得谐波分析中的核心开放问题。在本文中，我们考虑了Bôchner-riesz卷积内核的$ l^p $集成性，用于特定类别的品种（任何编成）。对于这些品种的子类，内核的$ l^p $集成性范围与相应的Bôchner-Riesz乘数运算符的$ l^p $边界范围有很大不同。
For a general compact variety $Γ$ of arbitrary codimension, one can consider the $L^p$ mapping properties of the Bôchner-Riesz multiplier $$ m_{Γ, α}(ζ) \ = \ {\rm dist}(ζ, Γ)^α ϕ(ζ) $$ where $α> 0$ and $ϕ$ is an appropriate smooth cut-off function. Even for the sphere $Γ= {\mathbb S}^{N-1}$, the exact $L^p$ boundedness range remains a central open problem in Euclidean Harmonic Analysis. In this paper we consider the $L^p$ integrability of the Bôchner-Riesz convolution kernel for a particular class of varieties (of any codimension). For a subclass of these varieties the range of $L^p$ integrability of the kernels differs substantially from the $L^p$ boundedness range of the corresponding Bôchner-Riesz multiplier operator.
