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Degree of Convergence of Some Operators Associated with Hardy-Littlewood Series for Functions of Class Lip(α, p), p > 1

In: Harmonic Analysis and Applications

Author

Listed:
  • Manish Kumar

    (Birla Institute of Technology and Sciences-Pilani)

  • Benjamin A. Landon

    (Daytona State College)

  • R. N. Mohapatra

    (University of Central Florida)

  • Tusharakanta Pradhan

    (Birla Institute of Technology and Sciences-Pilani)

Abstract

In this article, we study the degree of convergence of Euler, Borel, and (e, c) transforms of the Fourier series of functions of class Lip(α, p), for p > 1. When p tends to infinity, the results yield known results in the supremum norm studied by P. Sadangi (Sadangi, Degree of Convergence of functions in the Hölder metric, Ph.D. Thesis, Utkal University, 2006). The results of this chapter set the stage for further generalizations in other function spaces.

Suggested Citation

  • Manish Kumar & Benjamin A. Landon & R. N. Mohapatra & Tusharakanta Pradhan, 2021. "Degree of Convergence of Some Operators Associated with Hardy-Littlewood Series for Functions of Class Lip(α, p), p > 1," Springer Optimization and Its Applications, in: Michael Th. Rassias (ed.), Harmonic Analysis and Applications, pages 205-241, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-61887-2_9
    DOI: 10.1007/978-3-030-61887-2_9
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