On 28.09.2016 at 10.00 at the Institute seminar, associated professor Rza Ch. Mustafayev will give a talk on “Weak-type estimates in Morrey spaces for maximal commutator and commutator of maximal function”.

In this report we will discuss the unboundedness of the Hardy-Littlewood maximal operator M on Zygmund-Morrey space M_{L(logL), λ}(ℜⁿ), 0 < λ< n ,  as well as the boundedness of M on M_L(logL),λ(ℜⁿ) for radially decreasing functions and the boundedness of the iterated maximal operator  M²  from M_{L(logL), λ} (ℜⁿ) to weak Zygmund-Morrey space   WM_L(logL),λ (ℜⁿ) . The class of functions for which the maximal commutator C_b is bounded from M_L(logL),λ(ℜⁿ) to WM_L(logL),λ (ℜⁿ) is characterized. It is proved that the commutator of the Hardy-Littlewood maximal operator M with function  b ∈ BMO (ℜⁿ) such that b^–∈L_∞(ℜⁿ) is bounded from   M_{L(logL), λ}(ℜⁿ) to WM_L(logL),λ (ℜⁿ) .