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Kolmogorov-Type Inequalities for Periodic Functions Whose First Derivatives Have Bounded Variation

Authors:

Babenko V F Kofanov V A Pichugov S A

Institution:

(1) Dnepropetrovsk University, Dnepropetrovsk

Abstract:

We obtain a new unimprovable Kolmogorov-type inequality for differentiable 2 pgr

-periodic functions x with bounded variation of the derivative x prime

, namely

$\left\| {x'} \right\|_q \leqslant K\left( {q,p} \right)\left\| x \right\|_p^a \left( {\mathop V\limits_{0}^{{2\pi }} \left( {x'} \right)} \right)^{1 - {alpha }} ,$

where q

(0,

), p

], and

= min{1/2, p/q(p + 1)}.

Keywords:

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