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Hölder's inequality for functions of linearly dependent arguments

Florin Avram
Murad S. Taqqu

Abstract:

Consider functions with values in on a torus, in or in . These functions are allowed to have linearly dependent arguments. A generalized Hölder inequality for products of such functions is established. The proofs involve the use of convex polytypes associated with polymatroids and Riesz-Thorin interpolation theorem.