Approximation of functions from $L^{p}(\omega) _{\beta }$ by general linear operators of their Fourier series
Volume 95 / 2011
Banach Center Publications 95 (2011), 339-351
MSC: 42A24.
DOI: 10.4064/bc95-0-20
Abstract
We show the general and precise conditions on the functions and modulus of continuity as well as on the entries of matrices generating the summability means and give the rates of approximation of functions from the generalized integral Lipschitz classes by double matrix means of their Fourier series. Consequently, we give some results on norm approximation. Thus we essentially extend and improve our earlier results [Acta Comment. Univ. Tartu. Math. 13 (2009), 11–24] and the result of S. Lal [Appl. Math. Comput. 209 (2009), 346–350].
