This article is cited in 2 papers

Short communications

Multipliers of Fourier–Haar series in Lorentz spaces

N. T. Tleukhanova, A. N. Bashirova

Faculty of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, 13 Kazhymukan Munaitpasov St, Z01C0X0 Astana, Kazakhstan

Abstract: This article provides a complete description of the multipliers of the Fourier series along the Haar system in the Lorentz spaces $L_{p,r}$. Necessary and sufficient conditions are obtained ensuring that $\{\lambda_k^j\}_{k=0,j=1}^{\infty,2^k}\in m(L_{p,r}\to L_{q,s})$. This work generalizes and supplements the result of work [8].

Keywords and phrases: Fourier series, Haar system, Fourier series multipliers, Lorentz spaces.

MSC: 42B05, 46E30

Received: 01.08.2020

Language: English

DOI: 10.32523/2077-9879-2022-13-4-82-87

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