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Certain embedding theorems


We obtain necessary and sufficient conditions such that, for f(x) from LP(0, 1), the integral ∫ 0 1 ¦f (x)¦qdx (0<p<1,p<q<p(1 −p)−1) is convergent, or for f ε LP[0, 1] for all p ≥ 1, the integral ∫ 0 1 e¦f(x)¦dx is convergent.

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Translated from Matematicheskie Zametki, Vol. 19, No. 2, pp. 187–200, February, 1976.

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Storozhenko, É.A. Certain embedding theorems. Mathematical Notes of the Academy of Sciences of the USSR 19, 113–120 (1976).

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