论文标题
与操作员相关的平方功能的弱和强类型估计
Weak and strong types estimates for square functions associated with operators
论文作者
论文摘要
令$ l $为$ l^2（\ mathbb {r}^n）$中的线性运算符，该$生成一个semigroup $ e^{ - tl} $，其内核$ p_t（x，y）$满足高斯上限。在本文中，我们研究了与抽象操作员$ l $相关的几种锥形正方形功能的加权规范不等式$ s_ {α，l} $。我们首先建立了包括凸起估计的两重量不平等，以及任意权重的Fefferman-Stein不平等现象。我们还使用外推技术介绍了局部衰减估计，并通过Coifman-Fefferman的不平等现象估计了相应的Sawyer猜想。除此之外，我们考虑了其他弱类型估计值，包括$ s_ {α，l} $的受限弱型$（p，p）$以及$ s_ {α，l} $的换向器的端点估计值。最后，上述所有结论都可以应用于与$ l $相关的许多平方功能。
Let $L$ be a linear operator in $L^2(\mathbb{R}^n)$ which generates a semigroup $e^{-tL}$ whose kernels $p_t(x,y)$ satisfy the Gaussian upper bound. In this paper, we investigate several kinds of weighted norm inequalities for the conical square function $S_{α,L}$ associated with an abstract operator $L$. We first establish two-weight inequalities including bump estimates, and Fefferman-Stein inequalities with arbitrary weights. We also present the local decay estimates using the extrapolation techniques, and the mixed weak type estimates corresponding Sawyer's conjecture by means of a Coifman-Fefferman inequality. Beyond that, we consider other weak type estimates including the restricted weak-type $(p, p)$ for $S_{α, L}$ and the endpoint estimate for commutators of $S_{α, L}$. Finally, all the conclusions aforementioned can be applied to a number of square functions associated to $L$.
