论文标题
用粗糙内核的calderón换向器的定量加权边界
Quantitative weighted bounds for Calderón commutator with rough kernel
论文作者
论文摘要
我们考虑加权$ l^p（w）$有界（$ 1 <p <\ infty $和$ w $ a muckenhoupt $ a_p $重量）的calderón交换器$ \ MATHCALc_Ω$与粗糙的均质内核相关，在l^q（\ qustbb s^$ q $ qu $ quy）下$ q_0 $ a固定常数取决于$ W $。与先前相关的已知结果（假设$ω\在l^\ infty（\ mathbb s^{n-1}）$中，我们的结果是$ω\在l^q（\ mathbb s^{n-1}）中，$ q $在范围内$（q_0，\ infty）的$ q $是新的。我们还获得了$ l^p（w）$上的此$ \ MATHCALC_Ω$的定量加权绑定，这是该类别运营商的最著名定量结果。
We consider weighted $L^p(w)$ boundedness ($1<p<\infty $ and $w$ a Muckenhoupt $A_p$ weight) of the Calderón commutator $\mathcal C_Ω$ associated with rough homogeneous kernel, under the condition $Ω\in L^q(\mathbb S^{n-1})$ for $q_0<q\leq\infty$ with $q_0$ a fixed constant depending on $w$. Comparing to the previous related known results (assuming $Ω\in L^\infty(\mathbb S^{n-1})$), our result for $Ω\in L^q(\mathbb S^{n-1})$ with $q$ in the range $(q_0,\infty)$ is new. We also obtain a quantitative weighted bound for this $\mathcal C_Ω$ on $L^p(w)$, which is the best known quantitative result for this class of operators.
