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On exact constant in a one-dimensional embedding theorem

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Abstract:

In the case 1≤p<q≤∞, the question on the exact constant in the embedding of the space W _p ¹ (0,1) into the space L_q(0,1) is studied, i.e.,

$\min \frac{{||y||w_p^1 }}{{||y||L_q }} = \lambda _{pq} > 0,$

where the norm is defined by the equality $||y||_{W_p^1 }^P = ||y'||_{L_p }^P + ||y||_{L_p }^P$ . Bibliography: 5 titles. Translated fromProblemy Matematicheskogo Analiza, No. 19, 1999, pp. 149–163.

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