Multipliers of double Fourier-Haar series

The multipliers of double Fourier-Haar series for functions from anisotropic Lorentz spaces are investigated. Necessary and sufficient conditions are obtained for the sequence lambda = {lambda(j1j2)(k1k2)} to belong to the class m(L-(p) over bar,L-(r) over bar -> L-(q) over bar,L- (s) over bar). In particular, the case is described when (s) over bar<<(r)over bar>, which is a new result in the one-dimensional case as well.

Authors
Tleukhanova N.T.1 , Nursultanov E.D. 2, 3, 4 , Bashirova A.N.1
Journal
Advances in Operator Theory
Publisher
Tusi Mathematical Research Group (TMRG)
Number of issue
3
Language
English
Status
Published
DOI
10.1007/s43036-021-00148-z
Number
58
Volume
6
Year
2021
Organizations
  • 1 LN Gumilyov Eurasian Natl Univ, 13 Kazhymukan Munaitpasov St,Z01C0X0, Nur Sultan, Kazakhstan
  • 2 Moscow MV Lomonosov State Univ, Kazakhstan Branch, 11 Kazhymukan Munaitpasov St,Z01C0T6, Nur Sultan, Kazakhstan
  • 3 Inst Math & Math Modeling, 125 Pushkin Str,A26G7T4, Alma Ata, Kazakhstan
  • 4 RUDN Univ, 6 Miklukho Maklaya Str, Moscow 117198, Russia
Keywords
Fourier series; Haar system; Fourier series multipliers; Anisotropic Lorentz spaces
Date of creation
20.07.2021
Date of change
20.07.2021
Short link
https://repository.rudn.ru/en/records/article/record/74529/
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