The general methods which are powerful for the necessity of bounded commutators are given. As applications, some necessary conditions for bounded commutators are first obtained in certain endpoint cases, and several new characterizations of BM O spaces, Lipschitz spaces and their weighted versions via boundedness of commutators in various function spaces are deduced.2010 Mathematics Subject Classification. 42B20; 42B25.
Recommended by Nikolaos PapageorgiouLet μ be a nondoubling measure on R d . A class of commutators associated with multilinear fractional integrals and RBMO μ functions are introduced and shown to be bounded on product of Lebesgue spaces with μ.
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