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

Manish Kumar (), Benjamin A. Landon (), R. N. Mohapatra () and Tusharakanta Pradhan ()
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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

A chapter in Harmonic Analysis and Applications, 2021, pp 205-241 from Springer

Abstract: 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.

Keywords: 40A05; 41A10; 42A10 (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-030-61887-2_9

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DOI: 10.1007/978-3-030-61887-2_9

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