ORLICZ TYPE SPACES RELATED WITH NONLINEAR NONLOCAL FUNCTIONALS

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In the work we introduce the Orlicz spaces on the base of nonlinear nonlocal functionals. We study the main properties of such spaces. We prove that these spaces are Banach, separable and the set of compactly supported infinitely differentiable functions is dense in these spaces. We describe the structure of dual spaces and obtain the representations for the linear functionals.

Sobre autores

D. Borisov

Institute of Mathematics, Ufa Federal Research Center, RAS; Peoples Friendship University of Russia (RUDN University); Bashkir State Pedagogical University named after M. Akhmulla

Email: borisovdi@yandex.ru
Ufa, Russia; Moscow, Russia; Ufa, Russia

A. Piatnitskii

The Arctic University of Norway, campus Narvik; Higher School of Modern Mathematics MIPT

Email: apiatnitski@gmail.com
Narvik, Norway; Moscow, Russia

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