论文标题
弱取消操作员和奇异积分
Weakly canceling operators and singular integrals
论文作者
论文摘要
我们建议一种基本的谐波分析方法来取消和弱取消差分运算符，这允许将这些概念扩展到各向异性设置，并用傅立叶乘以轻度平滑度的规律性替代差异操作员。在这种各向异性傅立叶乘数的更普遍的环境中，我们证明了不平等$ \ | f \ | _ {l _ {l _ {\ infty}} \ sillsim \ | af | af | af | _ {l_1} $，如果$ a $是$ a $ a $ a $ a $ sever of dop $ d $ and a $ d $ __的clime $ d $ _2 \ | af \ | _ {l_1} $如果$ a $是订单$ \ frac {d} {2} $的取消操作员，则$ f $是$ d $变量中的函数。
We suggest an elementary Harmonic Analysis approach to canceling and weakly canceling differential operators, which allows to extend these notions to anisotropic setting and also replace differential operators with Fourier multiplies with mild smoothness regularity. In this more general setting of anisotropic Fourier multipliers, we prove the inequality $\|f\|_{L_{\infty}} \lesssim \|Af\|_{L_1}$ if $A$ is a weakly canceling operator of order $d$ and the inequality $\|f\|_{L_2} \lesssim \|Af\|_{L_1}$ if $A$ is a canceling operator of order $\frac{d}{2}$, provided $f$ is a function in $d$ variables.
