Approximation by T-Transformation of Double Walsh-Fourier Series to Multivariable Functions. (22nd April 2014) - Zhao, Yi; Yu, Dansheng
Abstract : We study the Walsh series expansion of multivariate functions in L p ( 1 ≤ p ≤ ∞ ) and, in particular, in L i p ( α, p ) . The rate of uniform approximation by T -transformation of rectangular partial sums of double Walsh to these functions is investigated. By extending the concepts of rest (head) bounded variation series, which was introduced by Leindler (2004), we generalize the related results of Móricz and Rhoades (1996), Nagy (2012). Our results can be applied to many summability methods, including the Nörlund summability and weighted summability.