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MR271724 (42 #6605) 46.38
Ilʹin, V. P. Conditions of validity of inequalities between $L\sb{p}$-norms of partial derivatives of functions of several variables. 1968 Trudy Mat. Inst. Steklov. 96 (1968), 205–242 (Russian); translated in Proc. Steklov Inst. Math., No. 96 (1968): Automat. Programming, Numer. Methods and Functional Anal. pp. 259–305 Amer. Math. Soc., Providence, R.I.
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