论文标题
与粗糙内核的最大和整体操作员重量的必要条件
Necessary condition on the weight for maximal and integral operators with rough kernels
论文作者
论文摘要
令$ 0 \ leqα<n $，$ m \ in \ mathbb {n} $，然后考虑$ t_ {α，m} $是整体操作员的a，由$ k（x，y）的内核给定，= k_1（x，y）= k_1（x-a_1y）k_2 k_2 k_2（x-a_2y）矩阵和每个$ k_i $满足分数尺寸和一般的分数Hörmander条件。在[Ibañez-Firnkorn，G。H.和Riveros，M。S.（2018）。某些具有Hörmander条件的分数型操作员。出现在安。学院。科学。芬恩。数学。证明，$ t_ {α，m} $由$ l^p（w）$ - norms，$ w \在a _ {\ infty} $中的$ w \，最大运算符的总和$ m_ {a_i { - { - { - 1}，α} $。在本文中，我们介绍了权重$ \ Mathcal {a} _ {a，p，q} $的类别，其中$ a $是可逆矩阵。该类是$ m_ {a^{ - 1}，α} $的弱型估计值的好权重。对于某些内核$ k_i $，我们可以表征$ t_ {α，m} $的强型估计值的权重。另外，我们使用测试条件给出了强型估计。
Let $0\leq α<n$, $m\in \mathbb{N}$ and let consider $T_{α,m}$ be a of integral operator, given by kernel of the form $$K(x,y)=k_1(x-A_1y)k_2(x-A_2y)\dots k_m(x-A_my),$$ where $A_i$ are invertible matrices and each $k_i$ satisfies a fractional size and generalized fractional Hörmander condition. In [Ibañez-Firnkorn, G. H., and Riveros, M. S. (2018). Certain fractional type operators with Hörmander conditions. To appear in Ann. Acad. Sci. Fenn. Math.] it was proved that $T_{α,m}$ is controlled in $L^p(w)$-norms, $w\in A_{\infty}$, by the sum of maximal operators $M_{A_i^{-1},α}$. In this paper we present the class of weights $\mathcal{A}_{A,p,q}$, where $A$ is an invertible matrix. This class are the good weights for the weak-type estimate of $M_{A^{-1},α}$. For certain kernels $k_i$ we can characterize the weights for the strong-type estimate of $T_{α,m}$. Also, we give a the strong-type estimate using testing conditions.
