The complete boundedness of singular integrals on weighted flag and product Hardy space

2025/06/29 by Tan, Jian
#42B25 #42B30 #46E30 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2506.23430

Abstract

It is known that product singular integrals are bounded on product Hardy spaces and that flag singular integrals are bounded on flag Hardy spaces. The purpose of this paper is to obtain the complete boundedness of singular integrals on weighted flag and product Hardy spaces. In particular, we prove the boundedness of one-parameter singular integrals on both weighted flag and product Hardy spaces, as well as the boundedness of flag singular integrals on weighted product Hardy spaces.

Citations

• Flag-like singular integrals and associated Hardy spaces on a kind of nilpotent Lie groups of step two
• Product Hardy spaces meet ball quasi-Banach function spaces
• Weak Hardy-Type Spaces Associated with Ball Quasi-Banach Function Spaces I: Decompositions with Applications to Boundedness of Calderón--Zygmund Operators
• Applications of Hardy Spaces Associated with Ball Quasi-Banach Function Spaces
• Maximal function, Littlewood--Paley theory, Riesz transform and atomic decomposition in the multi-parameter flag setting
• Discrete Littlewood-Paley-Stein theory and multi-parameter Hardy spaces associated with flag singular integrals

Related

• Singular integrals with product kernels associated with mixed homogeneities and Hardy spaces
• Boundedness of singular integrals on the flag Hardy spaces on Heisenberg group
• Characterizations of product Hardy spaces on stratified groups by singular integrals and maximal functions
• Some one-sided estimates for oscillatory singular integrals
• Boundedness of singular integral operators with variable kernels on weighted weak Hardy spaces