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Volume 29, Issue 2
Two Weighted $BMO$ Estimates for the Maximal Bochner-Riesz Commutator

Dan Zou, Xiaoli Chen & Dongxiang Chen

Anal. Theory Appl., 29 (2013), pp. 120-127.

Published online: 2013-06

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  • Abstract

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 $B^b_{\delta,\ast}$.

  • AMS Subject Headings

42B25, 42B30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{ATA-29-120, author = {Dan Zou , Xiaoli Chen , and Dongxiang Chen , }, title = {Two Weighted $BMO$ Estimates for the Maximal Bochner-Riesz Commutator}, journal = {Analysis in Theory and Applications}, year = {2013}, volume = {29}, number = {2}, pages = {120--127}, abstract = {

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 $B^b_{\delta,\ast}$.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2013.v29.n2.3}, url = {http://global-sci.org/intro/article_detail/ata/4520.html} }
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 $B^b_{\delta,\ast}$.

Dan Zou, Xiaoli Chen & Dongxiang Chen. (1970). Two Weighted $BMO$ Estimates for the Maximal Bochner-Riesz Commutator. Analysis in Theory and Applications. 29 (2). 120-127. doi:10.4208/ata.2013.v29.n2.3
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