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Matematicheskie Zametki, 1968, Volume 4, Issue 2, Pages 221–232
(Mi mzm6764)
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This article is cited in 6 scientific papers (total in 6 papers)
Exact constants in inequalities between norms of derivatives of functions
V. N. Gabushin V. A. Steklov Institute of Mathematics, Sverdlovsk Branch of the Academy of Sciences of USSR
Abstract:
In this article we shall concern ourselves with determining exact (least possible) constants in the inequalities of the form $\|f^{(k)}\|_{L_q}\le K\|f\|_{L_p}^{\frac{l-k-r^{-1}+q^{-1}}{l-r^{-1}+p^{-1}}}\|f^{(l)}\|_{L_r}^{\frac{k-q^{-1}+p^{-1}}{l-r^{-1}+p^{-1}}}$ for functions defined on the entire $(-\infty,\infty)$, absolutely continuous on any interval together with their $(l-1)$-th derivatives, and having finite
$$
l=2,\quad k=0,\quad k=1,\quad q=r=\infty,\quad 1\leqslant p<\infty
$$
is considered.
Received: 07.12.1967
Citation:
V. N. Gabushin, “Exact constants in inequalities between norms of derivatives of functions”, Mat. Zametki, 4:2 (1968), 221–232; Math. Notes, 4:2 (1968), 624–630
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https://www.mathnet.ru/eng/mzm6764 https://www.mathnet.ru/eng/mzm/v4/i2/p221
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Abstract page: | 436 | Full-text PDF : | 171 | First page: | 1 |
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