Abstract
We introduce and study spaces of functions on [0, ∞) which generalize the spaces of Stepanov. We derive multiplicative inequalities for the norms of derivatives of functions in these spaces.
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V. P. Glushko and S. G. Krein, “Inequalities for the norms of derivatives in the spaces Lp with a weight,” Sibirsk. Matem. Zh.,1, No. 3, 343–382 (1960).
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Translated from Matematicheskie Zametki, Vol. 6, No. 4, pp. 463–473, October, 1969.
In conclusion the author thanks S. G. Krein for his valuable advice and comments while the work on the present note was in progress.
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Kostin, V.A. Inequalities for the norms of derivatives in the spaces Lp,ϕ . Mathematical Notes of the Academy of Sciences of the USSR 6, 733–739 (1969). https://doi.org/10.1007/BF01093811
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DOI: https://doi.org/10.1007/BF01093811