论文标题
与拉普拉斯操作员在同质树上的热度半群的热量和下属的偶数收敛，并有两个加权$ l^p $最大不平等
Pointwise convergence of the heat and subordinates of the heat semigroups associated with the Laplace operator on homogeneous trees and two weighted $L^p$ maximal inequalities
论文作者
论文摘要
在本文中，我们考虑了由组合laplacian定义的热量半群$ \ {w_t \} _ {t> 0} $，在同质树上的$ \ {w_t \} _ {w_t \} _ {w_t \} _ {w_t \} _ {w_t \} _ {w_t \} _我们表征了$ x $上的权重$ u $，以上述家族的初始数据为l^{p}（p}（x，μ，u）$的初始数据，其中$ 1 \ le p <\ infty $，其中$μ$代表$ x $的计数。我们证明，$ x $中的这种收敛属性相当于以下事实：$ t \ in（0，r）$上的最大运算符，对于某些$ r> 0 $，由semogroup定义为$ l^{p}（p}（x，μ，x，μ，u）$ in $ l^{p}（x，x，x，μ，v）$ x $ x $ x上$
In this paper we consider the heat semigroup $\{W_t\}_{t>0}$ defined by the combinatorial Laplacian and two subordinated families of $\{W_t\}_{t>0}$ on homogeneous trees $X$. We characterize the weights $u$ on $X$ for which the pointwise convergence to initial data of the above families holds for every $f\in L^{p}(X,μ,u)$ with $1\le p<\infty$, where $μ$ represents the counting measure in $X$ . We prove that this convergence property in $X$ is equivalent to the fact that the maximal operator on $t\in (0,R)$, for some $R>0$, defined by the semigroup is bounded from $L^{p}(X,μ,u)$ into $L^{p}(X,μ,v)$ for some weight $v$ on $X$.
