SECOND DERIVATIVE TEST FOR ISOMETRIC EMBEDDINGS IN Lp
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چکیده
An old problem of P. Levy is to characterize those Banach spaces which embed isometrically in Lp. We show a new criterion in terms of the second derivative of the norm. As a consequence we show that, if M is a twice differentiable Orlicz function with M (0) = M (0) = 0, then the n-dimensional Orlicz space l M , n ≥ 3 does not embed isometrically in Lp with 0 < p ≤ 2. These results generalize and clear up the recent solution to the 1938 Schoenberg’s problem on positive definite functions.
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تاریخ انتشار 1997