Approximation of conjugate differentiable functions by their Abel–Poisson integrals

We obtain the exact values of upper bounds of approximations of classes of periodic conjugate differentiable functions by their Abel–Poisson integrals in uniform and integral metrics. Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 1, pp. 73–82, January, 2009.     

Complete Asymptotics of the Deviation of a Class of Differentiable Functions from the Set of Their Harmonic Poisson Integrals

On a class of differentiable functions W ^r and the class of functions conjugate to them, we obtain a complete asymptotic expansion of the upper bounds of deviations of the harmonic Poisson integrals of the functions considered.     

Approximation of (ψ, β)-Differentiable Functions Defined on the Real Axis by Abel-Poisson Operators

We obtain asymptotic equalities for upper bounds of approximations of functions on the classes and by Abel-Poisson operators. __________ Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 8, pp. 1097 – 1111, August, 2005.     

Approximation of functions from the class {\ifmmode\expandafter\hat\else\expandafter\^\fi{C}}^\psi_{\beta,\infty} by Poisson biharmonic operators in the uniform metric

We obtain asymptotic equalities for upper bounds of approximations of functions from the class by Poisson biharmonic operators in the uniform metric. Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 5, pp. 669–693, May, 2008.     

On the Approximation of Functions of the Hölder Class by Triharmonic Poisson Integrals

We determine the exact value of the upper bound for the deviation of the triharmonic Poisson integral from functions of the Hölder class.     

Approximation of (ψ, β)-differentiable functions by Poisson integrals in the uniform metric

We obtain asymptotic equalities for upper bounds of approximations of functions from the class C _β,∞^ψ by Poisson integrals in the metric of the space C.     

Approximation of conjugate differentiable functions by biharmonic Poisson integrals

We determine the exact values of upper bounds of approximations by biharmonic Poisson integrals on classes of conjugate differentiable functions in uniform and integral metrics.     

Approximation of functions from the classes $ C_{\beta, \infty }^\psi $ by biharmonic Poisson integrals

We deduce asymptotic equalities for the upper bounds of deviations of biharmonic Poisson integrals on the classes of (ψ, β)-differentiable periodic functions in the uniform metric.