Another View on the Hoelder Inequality

Details Another View on the Hoelder Inequality Another View on the Hoelder Inequality

2007-10-28

arxiv.org/abs/0710.5226v1

Mathematics

Functional Analysis

10 pages

Scientific paper

Every diagonalmatrix D yields an endomorphism on the n-dimensional complex vectorspace. If one provides this space with Hoelder norms, we can compute the operator norm of D. We define homogeneous weighted spaces as a generalization of normed spaces. We generalize the Hoelder norms for negative values, this leads to a proof of an extented version of the Hoelder inequality. Finally, we formulate this version also for measurable functions.

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