RATIONAL APPROXIMATIONS OF LIPSCHITZFUNCTIONS FROM THE HARDY CLASS ON THE LINE

Abstract

We study a rate of uniform approximations on the realline of summable Lipschitz functions f having a summable Hilbert transform H f by normalized logarithmic derivatives of rational functions. Inequalities between different metrics of the logarithmic derivatives of algebraic polynomials on the line are also considered.

Keywords

• logarithmic derivative of a rational function
• hilbert transform
• uniform approximation
• simple partial fraction
• inequality etween different metrics