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    A note on maximal commutators and commutators of maximal functions
    (Math Soc Japan, 2015) Agcayazi, Mujdat; Gogatishvili, Amiran; Koca, Kerim; Mustafayev, Rza
    In this paper maximal commutators and commutators of maximal functions with functions of bounded mean oscillation are investigated. New pointwise estimates for these operators are proved.
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    Weak-type Estimates in Morrey Spaces for Maximal Commutator and Commutator of Maximal Function
    (Tokyo Journal Mathematics Editorial Office Acad Center, 2018) Gogatishvili, Amiran; Mustafayev, Rza; Agcayazi, Mujdat
    In this paper it is shown that the Hardy-Littlewood maximal operator M is not bounded on Zygmund-Money space M-L(log L),M-lambda,M- O < lambda < n, but M is still bounded on M-L(logL),M-lambda for radially decreasing functions. The boundedness of the iterated maximal operator M-2 from M-L(log L),M-lambda to weak Zygmund-Morrey space WML(log L),lambda is proved. The class of functions for which the maximal commutator C-b is bounded from ML((log L),lambda)to WM(L(log L),lambda)are characterized. It is proved that the commutator of theHIardy-Littlewood maximal operator M with function b is an element of BMO(R-n)A such that b(-)is an element of L-infinity(R-n)A is bounded fom M(L(log L),lambda)to WM(L(log L),lambda. )New pointwise characterizations of M alpha M by means of norm of Hardy-Littlewood maximal function in classical Morrey spaces are given.