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

X. L. Chen & D. X. Chen

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

Published online: 2013-06

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  • Abstract
In this note, the authorprove that maximal Bocher-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 $1 &It p &It\infty$.The proof relies heavily on the pointwise estimates for the sharp maximal function of the commutator $B^b_{\delta,\ast}$.
  • Keywords

Bocher-Riesz operator commutator weighted BMO(w) space

  • AMS Subject Headings

42B25 42B30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{ATA-29-120, author = {X. L. Chen and D. X. 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 authorprove that maximal Bocher-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 $1 &It p &It\infty$.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 - X. L. Chen & D. X. 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 - Bocher-Riesz operator KW - commutator KW - weighted BMO(w) space AB - In this note, the authorprove that maximal Bocher-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 $1 &It p &It\infty$.The proof relies heavily on the pointwise estimates for the sharp maximal function of the commutator $B^b_{\delta,\ast}$.
X. L. Chen & D. X. 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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