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Approximation by trigonometric polynomials in variable exponent Morrey spaces

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Abstract

We investigate the direct and inverse theorems for trigonometric polynomials in the Morrey space \({{\mathcal {M}}}^{p(\cdot ),\lambda (\cdot )}\) with variable exponents. For this space, we obtain estimates of the K-functional in terms of the modulus of smoothness and the Bernstein type inequality for trigonometric polynomials.

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Acknowledgements

The authors would like to thank the referees for the helpful suggestions.

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Authors and Affiliations

  1. S.M. Nikol’skii Institute of Mathematics at RUDN University, Moscow, Russia

    Vagif S. Guliyev & Yoshihiro Sawano

  2. Institute of Mathematics and Mechanics, Baku, Azerbaijan

    Vagif S. Guliyev

  3. Department of Mathematics, Institute for Advanced studies in Basic Sciences (IASBS), Zanjan, Iran

    Arash Ghorbanalizadeh

  4. Department of Mathematics and Information Science, Tokyo Metropolitan University, Tokyo, Japan

    Yoshihiro Sawano

Authors
  1. Vagif S. Guliyev
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  2. Arash Ghorbanalizadeh
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  3. Yoshihiro Sawano
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Correspondence to Arash Ghorbanalizadeh.

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The authors declare that they have no conflict of interest.

Additional information

V. S. Guliyev: The research of V.S. Guliyev was partially supported by the grant of 1st Azerbaijan-Russia Joint Grant Competition (the Agreement number No. 18-51-06005). The research of V.S. Guliyev and Yoshihiro Sawano is partially supported by the Ministry of Education and Science of the Russian Federation (the Agreement number: 02.a03.21.0008). Yoshihiro Sawano is partially supported by 16K05209 JSPS.

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Guliyev, V.S., Ghorbanalizadeh, A. & Sawano, Y. Approximation by trigonometric polynomials in variable exponent Morrey spaces. Anal.Math.Phys. 9, 1265–1285 (2019). https://doi.org/10.1007/s13324-018-0231-y

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  • DOI: https://doi.org/10.1007/s13324-018-0231-y

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