论文标题
与Laguerre多项式扩展相关的强大空间的最大功能表征
Maximal function characterization of Hardy spaces related to Laguerre polynomial expansions
论文作者
论文摘要
在本文中，我们介绍了与非上加倍的概率度量$dγ_α（x）= \ frac {2x^{2x^{2α+1}}} {γ（α+1）unfty $dγ_α（x）= um， $ {α> - \ frac12} $。我们通过使用两个局部最大函数来获得$ \ Mathcal {H}^1（（0，\ infty），γ_α）$的特征。我们还证明，通过laguerre差分运算符生成的热半群定义的截断最大函数从$ \ Mathcal {h}^1（（（0，\ infty），γ_α），γ_α）$中限制为$ l^1（（0，\ infty），γ_α）$。
In this paper we introduce the atomic Hardy space $\mathcal{H}^1((0,\infty),γ_α)$ associated with the non-doubling probability measure $dγ_α(x)=\frac{2x^{2α+1}}{Γ(α+1)}e^{-x^2}dx$ on $(0,\infty)$, for ${α>-\frac12}$. We obtain characterizations of $\mathcal{H}^1((0,\infty),γ_α)$ by using two local maximal functions. We also prove that the truncated maximal function defined through the heat semigroup generated by the Laguerre differential operator is bounded from $\mathcal{H}^1((0,\infty),γ_α)$ into $L^1((0,\infty),γ_α)$.
