CHARACTERIZATIONS OF FUNCTIONS WITH HIGHER ORDER ...
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CHARACTERIZATIONS OF FUNCTIONS WITH HIGHER ORDER ...
tion for absolutely continuous functions with first derivatives in i£v: Theorem 1.1 (F. ... f1) Sponsored by the Mathematics Research Center, United States Army, Madison,. Wisconsin ..... 0, otherwise, and thus by the Markov-Bernstein theorem.
CHARACTERIZATIONS OF FUNCTIONS WITH HIGHER ORDER DERIVATIVES IN sev BY
J. W. JEROME AND L. L. SCHUMAKERO)
1. Introduction. In 1910 F. Riesz [3], [4] established the following characterization for absolutely continuous functions with first derivatives in i£v: Theorem 1.1 (F. Riesz). Let (a, b) be a possibly infinite interval in R. A necessary and sufficient condition that the function F be the integral of an element of the space yp(a, b), 1
