Convergence of generalized singular integrals to the unit, univariate case
In a recent paper, the second author (see ) studied the degree of uniform approximation to the unit in terms of uniform moduli of smoothness, by the Jackson-type generalizations of Picard and of Gauss-Weierstrass singular integrals. In this paper we consider the Lp-approximation, (1 ≤ p < +∞) by the above singular integrals in terms of the Lp-moduli of smoothness, and both uniform and Lp-approximation (in terms of the corresponding moduli of smoothness) by Jackson-type generalizations of the Poisson-Cauchy singular integrals.
Mathematical Inequalities and Applications
Anastassiou, G., & Gal, S. (2000). Convergence of generalized singular integrals to the unit, univariate case. Mathematical Inequalities and Applications, 3 (4), 511-518. https://doi.org/10.7153/mia-03-49