Gogatishvili, AmiranMustafayev, RzaAgcayazi, Mujdat2020-06-252020-06-252018Aǧcayazı, M., Gogatishvili, A., & Mustafayev, R. (2018). Weak-type estimates in Morrey spaces for maximal commutator and commutator of maximal function. Tokyo Journal of Mathematics, 41(1), 193-218.0387-3870https://doi.org/10.3836/tjm/1502179258https://hdl.handle.net/20.500.12587/7387Gogatishvili, Amiran/0000-0003-3459-0355; Gogatishvili, Amiran/0000-0003-3459-0355; Mustafayev, Rza/0000-0002-2806-9646In 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.eninfo:eu-repo/semantics/openAccessMorrey spacesmaximal operatorcommutatorBMOArticle41119321810.3836/tjm/15021792582-s2.0-85051184004Q4WOS:000439424800009Q4