On functions having coincident ρ-norms

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Date
2019-03-25
Journal Title
Journal ISSN
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Publisher
SISSA
Abstract
In a measure space (X;A; μ) we consider two measurable functions ƒ; g : E → R for some E ∈ A. We characterize the property of having equal p-norms when ρ varies in an infinite set P in [1;+∞). In a first theorem we consider the case of bounded functions when P is unbounded with ∑p∈P(1/p) = +∞ . The second theorem deals with the possibility of unbounded functions, when P has a finite accumulation point in [1, + ∞ ).
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13 pages
Keywords
Lebesgue integrable functions, Mellin transform
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