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The Inequalities for Polynomials and Integration over Fractal Arcs

Published:2001-03-01
Printed: Mar 2001
• B. A. Kats
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Abstract

The paper is dealing with determination of the integral $\int_{\gamma} f \,dz$ along the fractal arc $\gamma$ on the complex plane by terms of polynomial approximations of the function~$f$. We obtain inequalities for polynomials and conditions of integrability for functions from the H\"older, Besov and Slobodetskii spaces.