New Multilinear Littlewood--Paley g_λ^* Function and Commutator on weighted Lebesgue Spaces

2024/03/07 by Sun, Huimin, Yang, Shuhui, Lin, Yan
#42B25 #42B35 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2403.04285

Abstract

Via the new weight function A _p^θ(φ), the authors introduce a new class of multilinear Littlewood--Paley g_λ^* functions and establish the boundedness on weighted Lebesgue spaces. In addition, the authors obtain the boundedness of the multilinear commutator and multilinear iterated commutator generated by the multilinear Littlewood--Paley g_λ^* function and the new BMO function on weighted Lebesgue spaces. The results in this article include the known results in \citeXY2015,SXY2014. When m=1, that is, in the case of one-linear, our conclusions are also new, further extending the results in \citeS1961.

Related

• Multilinear Commutators of Multilinear Square Operators Associated with New BMO Functions and New Weight Functions
• Weighted Multilinear Square Function Bounds
• Boundedness of multilinear Littlewood--Paley operators with convolution type kernels on products of BMO spaces
• Multilinear Square Operators Meet New Weight Functions
• Littlewood-Paley equivalence and homogeneous Fourier multipliers