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The Inequalities for Polynomials and Integration over Fractal Arcs |
Canad. Math. Bull. 44(2001), 61-69
Published:2001-03-01
Printed: Mar 2001
Printed: Mar 2001
- B. A. Kats
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.
| MSC Classifications: |
26B15 - Integration: length, area, volume [See also 28A75, 51M25] 28A80 - Fractals [See also 37Fxx] |