Non-commutative Hardy–Littlewood maximal operator on symmetric spaces of τ -measurable operators
Nessipbayev Y. Tulenov K.
January 2021Birkhauser
Annals of Functional Analysis
2021#12Issue 1
In this paper, we investigate the Hardy–Littlewood maximal operator (in a sence of Bekjan) on non-commutative symmetric spaces. We obtain an upper distributional estimate (by means of the Cesàro operator) of a generalized singular number of the non-commutative Hardy–Littlewood maximal operator. We also show boundedness of the Hardy–Littlewood maximal operator from a general non-commutative symmetric space to another.
(Non-commutative) Lorentz and Marcinkiewicz spaces , Hardy–Littlewood maximal operator , Symmetric spaces of functions and operators , von Neumann algebra
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International Information Technology University, Almaty, 050040, Kazakhstan
Al-Farabi Kazakh National University, Almaty, 050040, Kazakhstan
Institute of Mathematics and Mathematical Modeling, Almaty, 050010, Kazakhstan
International Information Technology University
Al-Farabi Kazakh National University
Institute of Mathematics and Mathematical Modeling
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