Approximation by matrix transform means with respect to the character system of the group of 2-adic integers

Abstract

Abstract In this paper, we discuss the rate of the approximation by matrix transform means of Fourier series with respect to the character system of the group of 2-adic integers in L p ⁢ ( I ) {L^{p}(I)} spaces ( 1 ≤ p < ∞ {1\leq p<\infty} ) and in C ⁢ ( I ) {C(I)} . Moreover, we give an application for functions in Lipschitz classes Lip ⁢ ( α , p , I ) {\mathrm{Lip}(\alpha,p,I)} ( α > 0 {\alpha>0} , 1 ≤ p < ∞ {1\leq p<\infty} ) and Lip ⁢ ( α , C ⁢ ( I ) ) {\mathrm{Lip}(\alpha,C(I))} ( α > 0 {\alpha>0} ).