Weak-type estimates in Morrey spaces for maximal commutator and commutator of maximal function

0490765 - MÚ 2019 RIV JP eng J - Článek v odborném periodiku
Gogatishvili, Amiran - Mustafayev, R. - Agcayazi, M.
Weak-type estimates in Morrey spaces for maximal commutator and commutator of maximal function.
Tokyo Journal of Mathematics. Roč. 41, č. 1 (2018), s. 193-218. ISSN 0387-3870
Grant CEP: GA ČR GA13-14743S
Institucionální podpora: RVO:67985840
Klíčová slova: Morrey spaces * maximal operator * commutator
Obor OECD: Pure mathematics
Impakt faktor: 0.311, rok: 2018
https://projecteuclid.org/euclid.tjm/1513566018

In this paper it is shown that the Hardy-Littlewood maximal operator M is not bounded on Zygmund-Morrey space, but M is still bounded for radially decreasing functions. The boundedness of the iterated maximal operator M^2 from Zygmund-Morrey space to weak Zygmund-Morrey space is proved. The class of functions for which the maximal commutator C_b is bounded from Zygmund-Morrey space to weak Zygmund-Morrey space are characterized. It is proved that the commutator of the Hardy-Littlewood maximal operator M for BMO function b with bounded negative part is bounded from Zygmund-Morrey space to weak Zygmund-Morrey space. New pointwise characterizations of iteration of maximal and fractional maximal functions by means of norm of Hardy-Littlewood maximal function in classical Morrey spaces are given.
Trvalý link: http://hdl.handle.net/11104/0284915