Multipliers of double Fourier–Haar series
Tleukhanova N.T. Nursultanov E.D. Bashirova A.N.
July 2021Birkhauser
Advances in Operator Theory
2021#6Issue 3
The multipliers of double Fourier–Haar series for functions from anisotropic Lorentz spaces are investigated. Necessary and sufficient conditions are obtained for the sequence λ={λk1k2j1j2} to belong to the class m(Lp¯,r¯→ Lq¯,s¯). In particular, the case is described when s¯ < r¯ , which is a new result in the one-dimensional case as well.
Anisotropic Lorentz spaces , Fourier series , Fourier series multipliers , Haar system
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L.N. Gumilyov Eurasian National University, 13 Kazhymukan Munaitpasov St., Nur-Sultan, Z01C0X0, Kazakhstan
M.V. Lomonosov Moscow State University, Kazakhstan Branch, 11 Kazhymukan Munaitpasov St., Nur-Sultan, Z01C0T6, Kazakhstan
Institute of Mathematics and Mathematical Modeling, 125 Pushkin Str., Almaty, A26G7T4, Kazakhstan
RUDN University, 6 Miklukho-Maklaya Str., Moscow, 117198, Russian Federation
L.N. Gumilyov Eurasian National University
M.V. Lomonosov Moscow State University
Institute of Mathematics and Mathematical Modeling
RUDN University
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