Abstract:
A formula is obtained expressing the modulus of smoothness of the support
function of a set using the modulus of convexity of this set.
This formula
generalizes the well-known formula of J. Lindenstrauss that expresses the
modulus of smoothness of the dual space using the modulus of convexity of the
original space.
An exact relationship is obtained among the exponent of uniform
convexity of a set, the Hölder exponent for the derivative of its support
function, the exponent of smoothness of this support function, and other
exponents characterizing this set.
Keywords:modulus of convexity, modulus of
smoothness, uniform smoothness, uniform convexity, Lindenstrauss formula, support function.
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