Sharp Weighted Bounds for Multilinear Maximal Functions and Calderón–Zygmund Operators

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• 作者：Wendolín Damián ; Andrei K. Lerner…
• 关键词：Multilinear maximal operator ; Calderón–Zygmund theory ; Sharp weighted bounds ; 42B20 ; 42B25
• 刊名：Journal of Fourier Analysis and Applications
• 出版年：2015
• 出版时间：February 2015
• 年：2015
• 卷：21
• 期：1
• 页码：161-181
• 全文大小：386 KB
• 参考文献：1. Bennett, C., Sharpley, R.: Interpolation of Operators. Academic Press, New York (1988)
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  14. Lerner, A.K.: An elementary approach to several results on the Hardy–Littlewood maximal operator. Proc. Am. Math. Soc. 136(8), 2829-833 (2008) CrossRef
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  16. Lerner, A.K.: On an estimate of Calderón–Zygmund operators by dyadic positive operators. J. Anal. Math. 121, 141-61 (2013) CrossRef
  17. Lerner, A.K.: A simple proof of the \(A_2\) conjecture. Int. Math. Res. Not. IMRN 14, 3159-170 (2013)
  18. Lerner, A.K., Ombrosi, S., Pérez, C., Torres, R.H., Trujill
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Fourier Analysis
  Abstract Harmonic Analysis
  Approximations and Expansions
  Partial Differential Equations
  Applications of Mathematics
  Signal,Image and Speech Processing
  
• 出版者：Birkh盲user Boston
• ISSN：1531-5851

文摘

In this paper we prove some sharp weighted norm inequalities for the multi(sub)linear maximal function \(\mathcal {M}\) introduced in Lerner et al. (Adv Math 220:1222-264, 2009) and for multilinear Calderón–Zygmund operators. In particular we obtain a sharp mixed -span class="a-plus-plus inline-equation id-i-eq2"> \(A_p-A_{\infty }\) -bound for \(\mathcal {M}\) , some partial results related to a Buckley-type estimate for \(\mathcal {M}\) , and a sufficient condition for the boundedness of \(\mathcal {M}\) between weighted \(L^p\) spaces with different weights taking into account the precise bounds. Next we get a bound for multilinear Calderón–Zygmund operators in terms of dyadic positive multilinear operators in the spirit of the recent work (Lerner, J Anal Math 121:141-61, 2013). Then we obtain a multilinear version of the -span class="a-plus-plus inline-equation id-i-eq7"> \(A_2\) conjecture- Several open problems are posed.