TY - JOUR T1 - Two Weighted $BMO$ Estimates for the Maximal Bochner-Riesz Commutator AU - Dan Zou , AU - Xiaoli Chen , AU - Dongxiang Chen , JO - Analysis in Theory and Applications VL - 2 SP - 120 EP - 127 PY - 2013 DA - 2013/06 SN - 29 DO - http://doi.org/10.4208/ata.2013.v29.n2.3 UR - https://global-sci.org/intro/article_detail/ata/4520.html KW - Bochner-Riesz operator, commutator, weighted $BMO(\omega)$ space. AB -

In this note, the author prove that maximal Bochner-Riesz commutator $B^b_{\delta,\ast}$ generated by operator $B_{\delta,\ast}$ and  function $b\in BMO(\omega)$ is a bounded operator from $L^{p}(\mu)$ into $L^{p}(\nu)$, where $\omega\in(\mu\nu^{-1})^{\frac{1}{p}},\mu,\nu\in A_p$ for $1 < p <\infty$. The proof relies heavily on the pointwise estimates for the sharp maximal function of the commutator $B^b_{\delta,\ast}$.