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On approximation of functions in the spaces \(L_p \left( {\mathbb{R}^2 } \right)\) and \(L_p \left( {\mathbb{R}_{ + }^2 } \right)\) by generalized singular integrals with positive kernels

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References

  1. O. V. Besov, V. P. Il'in, and S. M. Nikol'skii, Integral Representations of Functions and Embedding Theorems [in Russian], Nauka, Moscow, 1996; English translation of the 1st ed.: Integral Representations of Functions and Embedding Theorems, Vols. I-II, New York, Wiley, 1978–1979.

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  2. N. Yu. Dododnov and V. V. Zhuk, “On approximate characteristics of functions of many variables occurring in saturation classes of continuity moduli of different order” [in Russian], Probl. Mat. Anal. 33 (2006), 79–90; English transl.: J. Math. Sci. New York 139 (2006), no. 1, 6323–6337.

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Correspondence to N. Yu. Dodonov.

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Translated from Problemy Matematicheskogo Analiza, No. 38, December 2008, pp. 23–36.

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Dodonov, N.Y., Zhuk, V.V. On approximation of functions in the spaces \(L_p \left( {\mathbb{R}^2 } \right)\) and \(L_p \left( {\mathbb{R}_{ + }^2 } \right)\) by generalized singular integrals with positive kernels. J Math Sci 156, 589–605 (2009). https://doi.org/10.1007/s10958-009-9276-7

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  • DOI: https://doi.org/10.1007/s10958-009-9276-7

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