Weighted estimates for vector-valued intrinsic square functions and commutators in the Morrey type spaces

2016/03/10 by Hua Wang, Wang, Hua
Mathematics · #Advanced Harmonic Analysis Research #Nonlinear Partial Differential Equations #Advanced Mathematical Physics Problems

paper · pdf · doi:10.48550/arxiv.1603.04657

Abstract

In this paper, the boundedness properties of vector-valued intrinsic square functions and their vector-valued commutators with BMO(\mathbb Rⁿ) functions are discussed. We first show the weighted strong type and weak type estimates of vector-valued intrinsic square functions in the Morrey type spaces. Then we obtain weighted strong type estimates of vector-valued analogues of commutators in Morrey type spaces. In the endpoint case, we establish the weighted weak Llog L-type estimates for these vector-valued commutators in the setting of weighted Lebesgue spaces. Furthermore, we prove weighted endpoint estimates of these commutator operators in Morrey type spaces. In particular, we can obtain strong type and endpoint estimates of vector-valued intrinsic square functions and their commutators in the weighted Morrey spaces and the generalized Morrey spaces.

Citations

• On functions of bounded mean oscillation
• On the solutions of quasi-linear elliptic partial differential equations

Related

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