On Holder’s Inequality in Lebesgue Spaces with Variable Order of Summability

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Abstract

In this paper, we introduce a new version of the definition of a quasi-norm (in particular, a norm) in Lebesgue spaces with variable order of summability. Using it, we prove an analogue of Holder’s inequality for such spaces, which is more general and more precise than those known earlier.

About the authors

V. I. Burenkov

Peoples’ Friendship University of Russia (RUDN University); Cardiff University

Author for correspondence.
Email: Burenkov@cardiff.ac.uk
Moscow, Russia; Cardiff, UK

T. V. Tararykova

Peoples’ Friendship University of Russia (RUDN University); Cardiff University

Email: tararykovat@cardiff.ac.uk
Moscow, Russia; Cardiff, UK

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