International Journal of Nonlinear Analysis and Applications
Approximation of Fourier series in terms of functions in $L_p$ Spaces for 0
Document Type : Research Paper
Authors
Mathematics Department, College of Education for pure Sciences, University of Babylon, Babylon, Iraq
Abstract
Many results introduced for the absolutely convergence of Fourier series in terms of absolutely continuous functions. Here we study the convergence of Fourier series in terms of $p$-integrable functions series.
Keywords
[1] S. Kaczmarz and H. Steinhaus, Theorie der orthogonalreihen, Monografie Mat., Tom 6, PWN, Warsaw, 1935; reprint, Chelsea, New York, 1951; Russian transl., Fizmatgiz, Moscow, 1958.
[2] P· Kahane, Series de Fourier absolument convergentes, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 50, Springer-Verlag, Berlin and New York, 1970.
[3] R. Salem, On a theorem of Zygmund, Duke Math. J. 10 (1943) 23–31.
[4] Y. Ul’yanov, P. Lavrent’evich, Solved and unsolved problems in the theory of trigonometric and orthogonal series, Russian Math. Sur. 19 (1964) 1–62.
[5] S. Vo Bockarev, On a problem of Zygmund, Izv. Akad. Nauk SSSR Ser. Mat. 37 (1973) 630–638.
[6] I. Wik, Criteria for absolute convergence of Fourier series of functions of bounded variation, Trans. Amer. Math. Soc. 163 (1971) 1–24.
[7] S. Yano, On a lemma of Marcinkiewicz and its applications to Fourier series, Tohoku Math. J. 2 (1959) 191–215.
[8] A. Zygmund, Remarque sur la convergence absolue des s´eries de Fourier, J. London Math. Soc. 1 (1928) 194–196.
Document Type : Research Paper
Authors
Mathematics Department, College of Education for pure Sciences, University of Babylon, Babylon, Iraq
Abstract
Many results introduced for the absolutely convergence of Fourier series in terms of absolutely continuous functions. Here we study the convergence of Fourier series in terms of $p$-integrable functions series.
Keywords
[1] S. Kaczmarz and H. Steinhaus, Theorie der orthogonalreihen, Monografie Mat., Tom 6, PWN, Warsaw, 1935; reprint, Chelsea, New York, 1951; Russian transl., Fizmatgiz, Moscow, 1958.
[2] P· Kahane, Series de Fourier absolument convergentes, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 50, Springer-Verlag, Berlin and New York, 1970.
[3] R. Salem, On a theorem of Zygmund, Duke Math. J. 10 (1943) 23–31.
[4] Y. Ul’yanov, P. Lavrent’evich, Solved and unsolved problems in the theory of trigonometric and orthogonal series, Russian Math. Sur. 19 (1964) 1–62.
[5] S. Vo Bockarev, On a problem of Zygmund, Izv. Akad. Nauk SSSR Ser. Mat. 37 (1973) 630–638.
[6] I. Wik, Criteria for absolute convergence of Fourier series of functions of bounded variation, Trans. Amer. Math. Soc. 163 (1971) 1–24.
[7] S. Yano, On a lemma of Marcinkiewicz and its applications to Fourier series, Tohoku Math. J. 2 (1959) 191–215.
[8] A. Zygmund, Remarque sur la convergence absolue des s´eries de Fourier, J. London Math. Soc. 1 (1928) 194–196.
[2] P· Kahane, Series de Fourier absolument convergentes, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 50, Springer-Verlag, Berlin and New York, 1970.
[3] R. Salem, On a theorem of Zygmund, Duke Math. J. 10 (1943) 23–31.
[4] Y. Ul’yanov, P. Lavrent’evich, Solved and unsolved problems in the theory of trigonometric and orthogonal series, Russian Math. Sur. 19 (1964) 1–62.
[5] S. Vo Bockarev, On a problem of Zygmund, Izv. Akad. Nauk SSSR Ser. Mat. 37 (1973) 630–638.
[6] I. Wik, Criteria for absolute convergence of Fourier series of functions of bounded variation, Trans. Amer. Math. Soc. 163 (1971) 1–24.
[7] S. Yano, On a lemma of Marcinkiewicz and its applications to Fourier series, Tohoku Math. J. 2 (1959) 191–215.
[8] A. Zygmund, Remarque sur la convergence absolue des s´eries de Fourier, J. London Math. Soc. 1 (1928) 194–196.
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Volume 12, Issue 2
November 2021Pages 897-911
- Receive Date: 08 March 2021
- Revise Date: 25 April 2021
- Accept Date: 04 May 2021