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On the coefficients of fourier series with respect to trigonometric systems in the space L 2,r

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Abstract

A Hardy-Littlewood type theorem for trigonometric series in the space L 2,r , strengthening Bochkarev’s theorem, is obtained.

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References

  1. S. V. Bochkarev, “The Hausdorff-Young-Riesz theorem in Lorentz spaces, and multiplicative inequalities,” in Trudy Mat. Inst. Steklov Vol. 219: Approximation Theory. Harmonic Analysis (Nauka, Moscow, 1997), pp. 103–114 [Proc. Steklov Inst.Math. 219 (4), 96–107 (1997)].

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  2. E. M. Stein, “Interpolation linear operators,” Trans. Amer.Math. Soc. 83, 482–492 (1956).

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Authors and Affiliations

  1. Eurasian National University, Astana, Kazakhstan

    N. T. Tleukhanova & G. K. Musabaeva

Authors
  1. N. T. Tleukhanova
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  2. G. K. Musabaeva
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Correspondence to N. T. Tleukhanova.

Additional information

Original Russian Text © N. T. Tleukhanova, G. K. Musabaeva, 2013, published in Matematicheskie Zametki, 2013, Vol. 94, No. 6, pp. 884–888.

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Tleukhanova, N.T., Musabaeva, G.K. On the coefficients of fourier series with respect to trigonometric systems in the space L 2,r . Math Notes 94, 908–912 (2013). https://doi.org/10.1134/S0001434613110278

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  • DOI: https://doi.org/10.1134/S0001434613110278

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