论文标题
抛物线操作员生成的分数泊松类型操作员的差分变换的界限
Boundedness of differential transforms for fractional Poisson type operators generated by parabolic operators
论文作者
论文摘要
在本文中，我们分析以下类型的$$ T_n^αf（x，t）= \ sum_ {j = n_1}^{n_2} v_j（p_ {a_ {a_ {j+1}}}^αf（x，x，x，x）-p_j}^a_j}^af（a _j}^αf（x，x，x，x，x）， r^{n+1}，\ n =（n_1，n_2）\ in \ mathbb z^2，\α> 0，$$，其中$ \ {p_τ^α\} _ {°{τ> 0} $是poisson-type poisson-type poisson-type $ $ l = $ l = \ n = $ l = \ n = \ n = \ l = \ n = - laplacian，$ \ {v_j \} _ {j \ in \ mathbb z} $一个有界的真实序列和$ \ {a_j \} _ {j \ in \ mathbb z} $ a增加的真实序列。 我们的分析将组成{}的有限性，在$ l^p（\ mathbb {r}^n）$中，以及$ bmo（\ mathbb {r}^n）$中的$ t^α_n$及其最大运算符及其最大运算符$ t^f（x） f（x）|。$ 还表明，最大差分转换运算符的局部大小与具有本地支持的功能$ f $的单数积分的顺序相同。此外，如果$ \ {v_j \} _ {j \ in \ mathbb z} \ in \ ell^p（\ mathbb z）$，我们在奇异积分的本地大小和硬质 - 小木材最大操作员之间获得了一个中间大小。
In this paper we analyze the convergence of the following type of series $$ T_N^αf(x,t)=\sum_{j=N_1}^{N_2} v_j(P_{a_{j+1}}^αf(x,t)-P_{a_j}^αf(x,t)),\quad (x,t)\in \mathbb R^{n+1}, \ N=(N_1, N_2)\in \mathbb Z^2,\ α>0, $$ where $\{P_τ^α\}_{τ>0}$ is the fractional Poisson-type operators generated by the parabolic operator $L=\partial_t-Δ$ with $Δ$ being the classical Laplacian, $\{v_j\}_{j\in \mathbb Z}$ a bounded real sequences and $\{a_j\}_{j\in \mathbb Z}$ an increasing real sequence. Our analysis will consist {of} the boundedness, in $L^p(\mathbb{R}^n)$ and in $BMO(\mathbb{R}^n)$, of the operators $T^α_N$ and its maximal operator $ T^*f(x)= \sup_{N\in \mathbb Z^2} |T^α_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. Moreover, if $\{v_j\}_{j\in \mathbb Z}\in \ell^p(\mathbb Z)$, we get an intermediate size between the local size of singular integrals and Hardy-Littlewood maximal operator.
