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Absolute convergence of the Fourier trigonometric series with gaps

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Published/Copyright: April 28, 2022
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Georgian Mathematical Journal
From the journal Georgian Mathematical Journal Volume 29 Issue 5

Abstract

In the present paper, the sufficient conditions are obtained for the generalized β-absolute convergence ( 0 < β < 2 ) of the Fourier trigonometric series with gaps for some classes of functions. In [8], analogous problems were considered for Fourier trigonometric series and sufficient conditions were established in terms of the δ-variation of a function; also, it was proved that these conditions are unimprovable in a certain sense. Our goal is to show that if a function f has a Fourier series with gaps, then the results obtained in [8] hold if the function f satisfies the derived conditions only on an arbitrarily small interval.

Keywords: Absolute convergence; Fourier series with gaps
MSC 2010: 42A20; 26A16

References

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Received: 2021-08-29
Revised: 2021-12-27
Accepted: 2022-01-27
Published Online: 2022-04-28
Published in Print: 2022-10-01

© 2022 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. On the well-posedness of the Cauchy problem with weight for systems of linear generalized ordinary differential equations with singularities
  3. On generalized derivations of semirings
  4. Non-smooth evolution of non-Newtonian flows influenced by thermal effects
  5. Ground states for fractional Choquard equations with magnetic fields and critical exponents
  6. A new class of exact solutions of von Karman’s equation in the nonlinear theory of gas dynamics
  7. Construction of certain new families related to q-Fubini polynomials
  8. Representation by degenerate Frobenius–Euler polynomials
  9. Absolute convergence of the Fourier trigonometric series with gaps
  10. Inverse of Berge’s maximum theorem in locally convex topological vector spaces and its applications
  11. On the negative order Cesáro summability of double series with respect to block-orthonormal systems
  12. Finiteness of meromorphic mappings from a complete Kähler manifold into a projective space
https://doi.org/10.1515/gmj-2022-2157
Keywords for this article
Absolute convergence; Fourier series with gaps

Articles in the same Issue

  1. Frontmatter
  2. On the well-posedness of the Cauchy problem with weight for systems of linear generalized ordinary differential equations with singularities
  3. On generalized derivations of semirings
  4. Non-smooth evolution of non-Newtonian flows influenced by thermal effects
  5. Ground states for fractional Choquard equations with magnetic fields and critical exponents
  6. A new class of exact solutions of von Karman’s equation in the nonlinear theory of gas dynamics
  7. Construction of certain new families related to q-Fubini polynomials
  8. Representation by degenerate Frobenius–Euler polynomials
  9. Absolute convergence of the Fourier trigonometric series with gaps
  10. Inverse of Berge’s maximum theorem in locally convex topological vector spaces and its applications
  11. On the negative order Cesáro summability of double series with respect to block-orthonormal systems
  12. Finiteness of meromorphic mappings from a complete Kähler manifold into a projective space
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