报告摘要：
| Suppose that $mathbb E:={E_r(x)}_{rin mathcal I, xin X}$ is a family of open subsets of a topological space $X$ endowed with a nonnegative Borel measure $mu$ satisfying certain basic conditions. We establish an $mathcal{A}_{mathbb E, p}$ weights theory with respect to $mathbb E$ and get the characterization of weighted weak type (1,1) and strong type $(p,p)$, $1
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