Presented at the 4th International Symposium on Innovative Approaches in Engineering and Natural Sciences (ISAS WINTER-2019 (ENS)), Samsun, Turkey, Nov 22, 2019

SETSCI Conference Proceedings, 2019, 9, Page (s): 16-18 , https://doi.org/10.36287/setsci.4.6.011

Published Date: 22 December 2019    | 978     16

The study of various mathematical problems (such as elasticity, non-Newtonian fluids and electrorheological fluids) with variable exponent growth condition has been received considerable attention in recent years. These problems are interesting in applications and raise many difficult mathematical problems. There are also a lot of published papers in these spaces. Vector-valued Lebesgue spaces are widely used in analysis, abstract evolution equations and in the theory of integral operators. In this paper we recall the weighted vector-valued classical and variable exponent Lebesgue spaces. We define a intersection space of vector-valued weighted classical Lebesgue and variable exponent Lebesgue spaces. We discuss some basic properties, such as, Banach space, dense subspaces and Hölder type inequalities of these spaces. We will also show that every elements of vector-valued these spaces are locally integrable. Moreover, we investigate several embeddings and continuous embeddings properties of these spaces under some conditions with respect to exponents and two weight functions.

Keywords - Vector-valued weighted classical and variable exponent Lebesgue spaces, locally integrable, continuous embedding.

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