OPTIMAL REARRANGEMENT-INVARIANT BANACH FUNCTION RANGE FOR THE HILBERT TRANSFORM
Tulenov K.S.
2021L.N. Gumilyov Eurasian National University
Eurasian Mathematical Journal
2021#12Issue 201 - 23 pp.
We describe the optimal rearrangement-invariant Banach function range of the classical Hilbert transform acting on a rearrangement-invariant Banach function space. We also show the existence of such optimal range for the Lorentz and Marcinkiewicz spaces.
Hilbert transform , optimal range , rearrangement-invariant Banach function space
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Department of Mechanics and Mathematics Al-Farabi Kazakh National University and Institute of Mathematics and Mathematical Modeling 71 Al-Farabi Ave, Almaty, 050040, Kazakhstan
Department of Mechanics and Mathematics Al-Farabi Kazakh National University and Institute of Mathematics and Mathematical Modeling 71 Al-Farabi Ave
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