AI 中文总结
研究齐型空间上分数次稀疏形式的双权估计，通过在放大球和二进方体上对弱反向Hölder不等式及稀疏检验进行归一化，引入\(\mathfrak d_Q^w\)，利用缺陷水平填充估计与双权检验得出混合弱\(A_{\infty}\)界。
AI 中文摘要
我们证明了齐型空间上分数次稀疏形式的双权估计。假设相关变换后的权属于弱\(A_{\infty}\)。弱反向Hölder不等式在放大球上归一化，而稀疏检验在二进方体上归一化。为衡量这种损失，引入\(\mathfrak d_Q^w := w(Q)/w(2\Lambda B_Q)\)。缺陷水平的填充估计与双权检验给出了所需的混合弱\(A_{\infty}\)界。
英文摘要
We prove two-weight estimates for fractional sparse forms on spaces of homogeneous type. The relevant transformed weights are assumed to belong to weak-$A_\infty$. The weak reverse Hölder inequality is normalized on enlarged balls, while sparse testing is normalized on dyadic cubes. To measure this loss, we introduce $\mathfrak d_Q^w:=w(Q)/w(2ΛB_Q)$. A packing estimate for the defect levels, combined with two-weight testing, gives the required mixed weak-$A_\infty$ bounds.
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