Békollé-Bonami权中的极大函数和Carleson测度
Maximal function and Carleson measures in Békollé-Bonami weights
摘要：
设$ω$为Békollé-Bonami权。本文给出了正测度$μ$的一个完整刻画，使得$$\int_{\mathcal H}|M_ωf(z)|^qdμ(z)\le C\left(\int_{\mathcal H}|f(z)|^pω(z)dV(z)\right)^{q/p}$$和$$μ\left(\{z\in \mathcal H: Mf(z)>λ\}\right)\le \frac{C}{λ^q}\left(\int_{\mathcal H}|f(z)|^pω(z)dV(z)\right)^{q/p}$$，其中$M_ω$是上半平面$\mathcal H$上的加权Hardy-Littlewood极大函数，而$1\le p,q<\infty$ .
英文摘要：
Let $ω$ be a Békollé-Bonami weight. We give a complete characterization of the positive measures $μ$ such that $$\int_{\mathcal H}|M_ωf(z)|^qdμ(z)\le C\left(\int_{\mathcal H}|f(z)|^pω(z)dV(z)\right)^{q/p}$$ and $$μ\left(\{z\in \mathcal H: Mf(z)>λ\}\right)\le \frac{C}{λ^q}\left(\int_{\mathcal H}|f(z)|^pω(z)dV(z)\right)^{q/p}$$ where $M_ω$ is the weighted Hardy-Littlewood maximal function on the upper-half plane $\mathcal H$, and $1\le p,q<\infty$.
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