Quantitative weighted estimates for the multilinear pseudo-differential operators in function spaces

2023/12/14 by Tan, Jiawei, Xue, Qingying
#42B20 #42B35 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2312.08938

Abstract

In this paper, the weighted estimates for multilinear pseudo-differential operators were systematically studied in rearrangement invariant Banach and quasi-Banach spaces. These spaces contain the Lebesgue space, the classical Lorentz space and Marcinkiewicz space as typical examples. More precisely, the weighted boundedness and weighted modular estimates, including the weak endpoint case, were established for multilinear pseudo-differential operators and their commutators. As applications, we show that the above results also hold for the multilinear Fourier multipliers, multilinear square functions, and a class of multilinear Calderón-Zygmund operators.

Related

• Multilinear pseudodifferential operators beyond Calderón-Zygmund theory
• Sharp weighted inequalities for iterated commutators of a class of multilinear operators
• Sharp weighted estimates for multi-linear Calder 'on-Zygmund operators\n on non-homogeneous spaces
• The boundedness of multilinear Calderón-Zygmund operators on weighted and variable Hardy spaces
• Weighted norm inequalities for multilinear operators and applications to multilinear Fourier multipliers