Weighted estimates for the multilinear maximal function on the upper half-spaces

2017/05/14 by Wei Chen, Chen, Wei, Chunxiang Zhu +1
Mathematics · #42B20 #42B25 #42B35 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1705.04939

openalex publication_date 2017/05/14 · openalex created_date 2017/05/26 · openalex updated_date 2026/07/28

Abstract

For a general dyadic grid, we give a Calderón-Zygmund type decomposition, which is the principle fact about the multilinear maximal function \mathfrakM on the upper half-spaces. Using the decomposition, we study the boundedness of \mathfrakM. We obtain a natural extension to the multilinear setting of Muckenhoupt's weak-type characterization. We also partially obtain characterizations of Muckenhoupt's strong-type inequalities with one weight. Assuming the reverse Hölder's condition, we get a multilinear analogue of Sawyer's two weight theorem. Moreover, we also get Hytönen-Pérez type weighted estimates.

Citations

• New maximal functions and multiple weights for the multilinear Calderón–Zygmund theory
• Some Maximal Inequalities
• A multilinear reverse Hölder inequality with applications to multilinear weighted norm inequalities

Related

• Sharp weighted bounds for multilinear maximal functions and Calderón-Zygmund operators
• Sharp weighted estimates for multi-linear Calder 'on-Zygmund operators\n on non-homogeneous spaces
• On two-weight norm estimates for multilinear fractional maximal function
• A weighted endpoint weak-type estimate for multilinear Calderón-Zygmund operators
• Two-weight inequalities for multilinear maximal functions in Orlicz spaces