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Imbedding theorems and geometric inequalities

V. S. Klimov


Abstract: Imbedding theorems for Sobolev spaces with a symmetric norm are established. In particular, the results obtained lead to new imbedding theorems for Orlich–Sobolev spaces. The proof of the basic results is based on geometric inequalities of the type of the classical Brunn–Minkovskii inequality.
Bibliography: 30 titles.

UDC: 513.881+517.5

MSC: Primary 46E30, 46E35; Secondary 52A40

Received: 27.02.1975

 English version: Mathematics of the USSR-Izvestiya, 1976, 10:3, 615–638

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