摘要
Starting with the relatively simple observation that the variational estimates of the commutators of the standard Calderón-Zygmund operators with the bounded mean oscillation(BMO)functions can be obtained from their weighted variational estimates,we establish the similar variational estimates for the commutators of the BMO functions with rough singular integrals,which do not admit any weighted variational estimates.The proof involves several Littlewood-Paley-type inequalities with the commutators as well as Bony decomposition and related para-product estimates.
基金
supported by National Natural Science Foundation of China(Grant Nos.11871096,11471033,11571160 and 11601396)
Thousand Youth Talents Plan of China(Grant No.429900018101150(2016))
Funds for Talents of China(Grant No.413100002)
the Fundamental Research Funds for the Central Universities and Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20130003110003)。
