IJPAM: Volume 82, No. 3 (2013)
COEFFICIENTS OF FUNCTIONS OF BOUNDED -VARIATION
Department of Mathematics
Faculty of Science
The Maharaja Sayajirao University of Baroda
Vadodara, 390 002 (Gujarat), INDIA
Abstract. For a Lebesgue integrable complex-valued function defined over the -dimensional torus , let denote the multiple Walsh-Fourier coefficient of , where , . The Riemann-Lebesgue lemma shows that as for any . However, it is known that, these Fourier coefficients can tend to zero as slowly as we wish. When the definitive results are due to B. L. Ghodadra and J. R. Patadia [J. Inequal. Pure Appl. Math., 9 (2) (2008), Article 44] for functions of certain classes of functions of generalized bounded variation. Ghodadra [Acta Math. Hungar 128 (4), 2010, 328-343] defined the notion of bounded -variation () for a function from a rectangle to and obtained definitive results for the order of magnitude of multiple trigonometric Fourier coefficients. In this paper, such definitive results for the order of magnitude of multiple Walsh-Fourier coefficients for a function of bounded -variation are obtained.
Received: September 4, 2012
AMS Subject Classification: 42C10, 42B05, 26B30, 26D15
Key Words and Phrases: multiple Walsh-Fourier coefficient, function of bounded -variation in several variables, order of magnitude
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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395