ON EMBEDDING INTO LORENTZ SPACES (A DISTANT CASE)
Baidaulet A.T. Suleimenov K.M.
2024Institute of Mathematics with Computing Centre
Ufa Mathematical Journal
2024#16Issue 21 - 14 pp.
In the work we study an upper bound for a (Formula presented) n increasing non negative function in the space (Formula presented) by the modulus of continuity of a variable increment (Formula presented). We show that for the increment of the function of form (Formula presented) in the bound the modulus of continuity casts into the form (Formula presented). We also study the embedding (Formula presented) (a distant case). We obtained necessary and sufficient conditions for the parameters (Formula presented) and the functions (Formula presented) for this embedding.
classes of functions , Lorentz spaces , modulus of continuity of variable increment , non–increasing permutation of the function
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L.N. Gumilyov Eurasian National University, Kazhymukan str. 13, Astana, 010000, Kazakhstan
L.N. Gumilyov Eurasian National University
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