Estimates of the norms of some cosine and sine series
Estimates of the norms of some cosine and sine series
In the work we estimate the $\mathbb{L}^1$ norms of some special cosine and sine series used in studying fractional integrals.
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- N. K. Bari: Trigonometric Series, Moscow (in Russian, 1961).
- R. G. Bartle: The Elements of Integration, John Wiley and Sons, Inc., New York-London-Sydney (1966).
- 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.
- 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.
- P. L. Butzer, R. J. Nessel: Fourier Analysis and Approximation, New York-Basel (1971).
- 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.
- 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.
- J.W. Garrett, Cˇ . V. Stanojevic´: On $\mathbb{L}^1$ convergence of certain cosine sums, Proc. Amer.Math. Soc., 54 (1976), 101–105.
- M. Izumi, Sh. Izumi: On some trigonometrical polynomials, Math. Scand., 21 (1967), 38–44.
- I. P. Natanson: Constructive Function Theory. Vol I, Frederick Ungar Publ., New York (1964).
- B. Szal: On L-convergence of trigonometric series, J. Math. Anal. Appl., 373(2) (2011), 449–463.
- Z. Tomovski: Convergence and integrability for some classes of trigonometric series, Dissertationes Math (Rozprawy Mat.), 420 (2003), 65 pp.
- W. H. Young: On a certain series of Fourier, Proc. London Math. Soc., 11 (1913), 357–366.
- A. Zygmund: Trigonometric series, Third Edition, Vol I and II combined, Cambridge Mathematical Library (2002).