On Holder's inequality in Lebesgue spaces with variable order of summability

V. I. Burenkov^ab, T. V. Tararykova<sup>ab

a</sup> Peoples' Friendship University of Russia (RUDN University), Moscow, Russia
^b Cardiff University, Cardiff, UK

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 Hölder's inequality for such spaces, which is more general and more precise than those known earlier.

UDC: 517.518

DOI: 10.22363/2413-3639-2021-67-3-472-482