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

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Abstract

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 Lp̄[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.

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Authors and Affiliations

  1. L. N. Gumilyov Eurasian National University, 13 Kazhymukan Munaitpasov St., Nur-Sultan, Z01C0X0, Kazakhstan

    A. N. Bashirova

  2. M. V. Lomonosov Moscow State University, Kazakhstan Branch, 11 Kazhymukan Munaitpasov St., Nur-Sultan, Z01C0T6, Kazakhstan

    E. D. Nursultanov

Authors
  1. A. N. Bashirova
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  2. E. D. Nursultanov
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Correspondence to E. D. Nursultanov.

Additional information

This work was supported by the Ministry of Education and Science of the Republic of Kazakhstan (Grant AP08856479).

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Bashirova, A.N., Nursultanov, E.D. The Hardy—Littlewood theorem for double Fourier—Haar series from mixed metric Lebesgue Lp̄[0, 1]2 and net Np̄, q̄(M) spaces. Anal Math 48, 5–17 (2022). https://doi.org/10.1007/s10476-022-0115-0

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  • DOI: https://doi.org/10.1007/s10476-022-0115-0

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