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The Inequalities for Polynomials and Integration over Fractal Arcs

Open Access article
 Printed: Mar 2001
  • B. A. Kats
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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.
MSC Classifications: 26B15, 28A80 show english descriptions Integration: length, area, volume [See also 28A75, 51M25]
Fractals [See also 37Fxx]
26B15 - Integration: length, area, volume [See also 28A75, 51M25]
28A80 - Fractals [See also 37Fxx]

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