论文标题
与拉瓜多项式扩展相关的谐波分析运算符的端点估计值
Endpoint estimates for harmonic analysis operators associated with Laguerre polynomial expansions
论文作者
论文摘要
在本文中，我们给出了一个标准，以证明几位运营商的界限结果（（（0，\ infty），γ_α）$至$ l^1（（0，\ infty），γ_α）$，也来自$ l^\ infty（（（0，\ infty），γ_α），γ_α）$ to y Infty（0，\ infty）测量$dγ_α（x）= \ frac {2} {γ（α+1）} x^{2α+1} e^{ - x^2} dx $ on $（0，\ infty）$时，$ {α> - \ frac12} $。我们将使用它来建立Riesz变换，最大运算符，Littlewood-Paley功能，Laplace Transform类型的乘数，Laguerre设置中的分数积分和变异算子的端点估计值。
In this paper we give a criterion to prove boundedness results for several operators from $H^1((0,\infty),γ_α)$ to $L^1((0,\infty),γ_α)$ and also from $L^\infty((0,\infty),γ_α)$ to $\BMO((0,\infty),γ_α)$, with respect to the probability measure $dγ_α(x)=\frac{2}{Γ(α+1)} x^{2α+1} e^{-x^2} dx$ on $(0,\infty)$ when ${α>-\frac12}$. We shall apply it to establish endpoint estimates for Riesz transforms, maximal operators, Littlewood-Paley functions, multipliers of Laplace transform type, fractional integrals and variation operators in the Laguerre setting.
