On constants in some inequalities for intermediate derivatives on a finite interval |
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Authors: | Semyon Rafalson |
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Institution: | John Jay High School, 237 Seventh Avenue, Brooklyn, NY 11215, USA |
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Abstract: | Let Lq (1 q<∞) be the space of functions f measurable on I=−1,1] and integrable to the power q, with norm L∞ is the space of functions measurable on I with norm We denote by AC the set of all functions absolutely continuous on I. For n N, q 1,∞] we setWn,q={f:f(n−1) AC, f(n) Lq}.In this paper, we consider the problem of accuracy of constants A, B in the inequalities (1)|| f(m)||q A|| f||p+B|| f(m+k+1)||r, m N, k W; p,q,r 1,∞], f Wm+k+1,r. |
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