The Hardy—Littlewood theorem for double Fourier—Haar series from mixed metric Lebesgue L[0, 1]2 and net Np̄, q̄(M) spaces


Bashirova A.N. Nursultanov E.D.
March 2022Springer Science and Business Media B.V.

Analysis Mathematica
2022#48Issue 15 - 17 pp.

We obtain a criterion given in terms of the Fourier-Haar co-efficients for the function f(x1, x2) to belong to the net space Np̄, q̄(M) and to the Lebesgue space L[0, 1]2 with mixed metric, where 1 < p̄ < ∞,0 < q̄ ≤ ∞, p̄ =(p1, p2), q̄=(q1, q2) and M is the set of all rectangles in ℝ2. We prove the Hardy-Littlewood theorem for multiple Fourier-Haar series.

anisotropic space , Fourier series , Haar system , Lebesgue space , net space

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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

L. N. Gumilyov Eurasian National University
M. V. Lomonosov Moscow State University

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