Characterization of two-weighted inequalities for multilinear fractional maximal operator

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• 作者：Mingming Cao ^{m.cao@mail.bnu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Qingying Xue ; ^{qyxue@bnu.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Multilinear fractional maximal operator ; Two-weight inequalities ; Tent space ; S(p&rarr ; q) condition ; B(p&rarr ; q) condition
• 刊名：Nonlinear Analysis
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：130
• 期：Complete
• 页码：214-228
• 全文大小：696 K

文摘

In this paper, we restudied the two-weight problem of multilinear fractional maximal operator M_α${\mathcal{M}}_{\alpha }$. First, we gave a characterization of two-weight inequalities for M_α${\mathcal{M}}_{\alpha }$ related to a multilinear analogue of Sawyer’s two-weight condition $S_{(\overrightarrow{p},q)}$, which essentially improved and extended some known results before. This was done mainly by using the technique of the well known atomic decomposition of tent space. Then we obtained the strong boundedness of M_α${\mathcal{M}}_{\alpha }$ associated with multiple weight $A_{(\overrightarrow{p},q)}$ class, which removed the power bump condition assumed in the known results before. Finally, a new two-weight $B_{(\overrightarrow{p},q)}$ condition was introduced and the two-weight inequality of M_α${\mathcal{M}}_{\alpha }$ with $B_{(\overrightarrow{p},q)}$ condition was established.