Abstract
Устанавливается сле дующее неравенство т ипа неравенства Турана. П усть 0<p<q<∞, 1−1/p+1/p≥0. Еслиf(x) — де йствительный алгебраический многочлен степени не вышеn, все нули которо го лежат на [−1,1], то $$\left( {\int_{ - 1}^1 {\left| {f'(x)} \right|^p dx} } \right)^{1/p} \geqslant C^* \sqrt n ^{1 - 1/p + 1/q} \left( {\int_{ - 1}^1 {\left| {f(x)} \right|^q dx} } \right)^{1/q} .$$ Эта работа завершает цикл исследований ав тора, относящихся к этой за даче.
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