Research Article

Estimates of the norms of some cosine and sine series

Volume: 6 Number: 3 September 15, 2023
EN

Estimates of the norms of some cosine and sine series

Abstract

In the work we estimate the $\mathbb{L}^1$ norms of some special cosine and sine series used in studying fractional integrals.

Keywords

References

  1. N. K. Bari: Trigonometric Series, Moscow (in Russian, 1961).
  2. R. G. Bartle: The Elements of Integration, John Wiley and Sons, Inc., New York-London-Sydney (1966).
  3. A. S. Belov: On the unimprovability of some theorems on the convergence in the mean of trigonometric series, J. Math. Sci. (N.Y.), 250(3) (2020), 404–418.
  4. G. Brown, K. Y. Wang and D. C. Wilson: Positivity of some basic cosine sums, Math. Proc. Cambridge Philos. Soc., 114(3) (1993), 383–391.
  5. P. L. Butzer, R. J. Nessel: Fourier Analysis and Approximation, New York-Basel (1971).
  6. P. L. Butzer, U.Westphal: An access to fractional differentiation via fractional difference quotients, Fractional Calculus and Its Applications, Lecture Notes in Mathematics, 457 (1975), 116–145.
  7. J. W. Garrett, Cˇ . V. Stanojevic´: Necessary and sufficient conditions for $\mathbb{L}^1$ convergence of trigonometric series, Proc. Amer. Math. Soc., 60 (1976), 68–71.
  8. J.W. Garrett, Cˇ . V. Stanojevic´: On $\mathbb{L}^1$ convergence of certain cosine sums, Proc. Amer.Math. Soc., 54 (1976), 101–105.

Details

Primary Language

English

Subjects

Lie Groups, Harmonic and Fourier Analysis

Journal Section

Research Article

Early Pub Date

August 18, 2023

Publication Date

September 15, 2023

Submission Date

August 17, 2023

Acceptance Date

August 18, 2023

Published in Issue

Year 2023 Volume: 6 Number: 3

APA
Bustamante, J. (2023). Estimates of the norms of some cosine and sine series. Constructive Mathematical Analysis, 6(3), 142-150. https://doi.org/10.33205/cma.1345440
AMA
1.Bustamante J. Estimates of the norms of some cosine and sine series. CMA. 2023;6(3):142-150. doi:10.33205/cma.1345440
Chicago
Bustamante, Jorge. 2023. “Estimates of the Norms of Some Cosine and Sine Series”. Constructive Mathematical Analysis 6 (3): 142-50. https://doi.org/10.33205/cma.1345440.
EndNote
Bustamante J (September 1, 2023) Estimates of the norms of some cosine and sine series. Constructive Mathematical Analysis 6 3 142–150.
IEEE
[1]J. Bustamante, “Estimates of the norms of some cosine and sine series”, CMA, vol. 6, no. 3, pp. 142–150, Sept. 2023, doi: 10.33205/cma.1345440.
ISNAD
Bustamante, Jorge. “Estimates of the Norms of Some Cosine and Sine Series”. Constructive Mathematical Analysis 6/3 (September 1, 2023): 142-150. https://doi.org/10.33205/cma.1345440.
JAMA
1.Bustamante J. Estimates of the norms of some cosine and sine series. CMA. 2023;6:142–150.
MLA
Bustamante, Jorge. “Estimates of the Norms of Some Cosine and Sine Series”. Constructive Mathematical Analysis, vol. 6, no. 3, Sept. 2023, pp. 142-50, doi:10.33205/cma.1345440.
Vancouver
1.Jorge Bustamante. Estimates of the norms of some cosine and sine series. CMA. 2023 Sep. 1;6(3):142-50. doi:10.33205/cma.1345440

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