2017
Том 69
№ 6

All Issues

Weighted Estimates for Multilinear Commutators of Marcinkiewicz Integrals with Bounded Kernel

Liu Qingguo, Wu Jianglong

Full text (.pdf)


Abstract

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.

English version (Springer): Ukrainian Mathematical Journal 66 (2014), no. 4, pp 602-616.

Citation Example: Liu Qingguo, Wu Jianglong Weighted Estimates for Multilinear Commutators of Marcinkiewicz Integrals with Bounded Kernel // Ukr. Mat. Zh. - 2014. - 66, № 4. - pp. 538–550.

Full text