Commutators of vector-valued intrinsic square functions on vector-valued generalized weighted Morrey spaces

2013/12/19 by Guliyev, Vagif S., Omarova, M. N.
#42B25 #42B35 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1312.5587

Abstract

In this paper, we will obtain the strong type and weak type estimates for vector-valued analogues of intrinsic square functions in the generalized weighted Morrey spaces M^Φ,φ_w(ℝⁿ). We study the boundedness of intrinsic square functions including the Lusin area integral, Littlewood-Paley g-function and g_λ^* -function and their commutators on vector-valued generalized weighted Morrey spaces M^Φ,φ_w(l₂). In all the cases the conditions for the boundedness are given either in terms of Zygmund-type integral inequalities on φ(x,r) without assuming any monotonicity property of φ(x,r) on r.

Related

• Weighted estimates for vector-valued intrinsic square functions and commutators in the Morrey type spaces
• Boundedness of vector-valued intrinsic square functions in Morrey type spaces
• Boundedness of intrinsic square functions and their commutators on generalized weighted Orlicz-Morrey spaces
• Intrinsic square functions on the weighted Morrey spaces
• Boundedness of intrinsic square functions on generalized Morrey spaces