论文标题
贝塞尔操作员生成的泊松半群的差分变换的界限
Boundedness of differential transforms for Poisson semigroups generated by Bessel operators
论文作者
论文摘要
在本文中，我们分析以下类型的系列类型\ begin {equion*} t_n f（x）= \ sum_ {j = n_1}^{n_2}^{n_2} v_j \ big（\ mathcal {p} _ {p} ________________ {a__ {j+1}}}}}} f（x） - \ Mathc}} f（x）\ big），\ quad x \ in \ mathbb r_+，\ end {equation*}其中$ \ {\ Mathcal {p} _t _t \} _ {t> 0} $是Bessel操作员的POISSON SEMORGOUP dx^2} - {2λ\ fover x} {d \ over dx} $，$λ$为正常数，$ n =（n_1，n_2）\ in \ mathbb z^2 $带有$ n_1 <n_1 <n_2，$ n_1 <n_1 <n_1 <n_1 <n_1 <n_2，$ \ $ \ $ \ \ \ \ {v_j \} $ { $ \ {a_j \} _ {j \ in \ mathbb z} $是一个增加的真实序列。 {我们的分析将以限制性为组成，在$ l^p（\ m athbb {r} _+）$中，以及$ bmo（\ mathbb {r} _+）$的$ t_n $及其最大运营商$ t^*f（x）= sup_n \ abs abs {t_n f（x）simiim sige y sige and simim sige y Maves ysim and simal and inim simal and t_n $及其最大运营商$ t^*f（x）= $。转换操作员与具有本地支持的功能$ f $的单数积分的顺序相同。
In this paper we analyze the convergence of the following type of series \begin{equation*} T_N f(x)=\sum_{j=N_1}^{N_2} v_j\Big(\mathcal{P}_{a_{j+1}} f(x)-\mathcal{P}_{a_{j}} f(x)\Big),\quad x\in \mathbb R_+, \end{equation*} where $\{\mathcal{P}_t \}_{t>0}$ is the Poisson semigroup of the Bessel operator $\displaystyle Δ_λ:=-{d^2\over dx^2}-{2λ\over x}{d\over dx}$ with $λ$ being a positive constant, $N=(N_1, N_2)\in \mathbb Z^2$ with $N_1<N_2,$ $\{v_j\}_{j\in \mathbb Z}$ is a bounded real sequences and $\{a_j\}_{j\in \mathbb Z}$ is an increasing real sequence. {Our analysis will consist in the boundedness, in $L^p(\mathbb{R}_+)$ and in $BMO(\mathbb{R}_+)$, of the operators $T_N$ and its maximal operator $ T^*f(x)= sup_N \abs{T_N f(x)}.$} It is also shown that the local size of the maximal differential transform operators is the same with the order of a singular integral for functions $f$ having local support.
