Ukrainian Mathematical Journal

, Volume 66, Issue 4, pp 602–616 | Cite as

Weighted Estimates for Multilinear Commutators of Marcinkiewicz Integrals with Bounded Kernel

  • Jianglong Wu
  • Qingguo Liu
Let \( {\mu}_{\varOmega, \overrightarrow{b}} \) be a multilinear commutator generalized by the n-dimensional Marcinkiewicz integral with bounded kernel μ Ώ and let \( {b}_j\ \in Os{c_{\exp}}_{L^{r_j}} \) , 1 ≤ jm. We prove the following weighted inequalities for ωA and 0 < p < ∞:
$$ {\begin{array}{cc}\hfill {\left\Vert {\mu}_{\varOmega }(f)\right\Vert}_{L^p\left(\omega \right)}\le C{\left\Vert M(f)\right\Vert}_{L^p\left(\omega \right)},\hfill & \hfill \left\Vert {\mu}_{\varOmega, \overrightarrow{b}}(f)\right\Vert \hfill \end{array}}_{L^p\left(\omega \right)}\le C{\left\Vert {M}_{L{\left( \log L\right)}^{1/r}}(f)\right\Vert}_{L^p\left(\omega \right)}. $$

The weighted weak L(log L)1/r -type estimate is also established for p =1 and ωA 1.


Compact Support Orlicz Space Degree Zero Type Estimate Bound Kernel 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Jianglong Wu
    • 1
  • Qingguo Liu
    • 2
  1. 1.Mudanjiang Normal UniversityMudanjiangChina
  2. 2.University of Nova GoricaNova GoricaSlovenia

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