As a generalisation of constant Lebesgue spaces, variable exponent Lebegue spaces go back many years, and in subsequent decades variable Lebesgue and Sobolev spaces have been systematically investigated. Since then, many variable exponent real function spaces and complex function spaces have appeared, such as Besov spaces, Trieble-Lizorkin spaces, Hardy spaces, Bessel potential spaces, Herz spaces, Morrey spaces, Herz-Morrey spaces, Bergman spaces, and Fock spaces with variable exponents.

For three decades, variable exponent function spaces have been widely applied in differential equations, image processing, and approximation theory, and many variable exponent real function spaces and complex function spaces have appeared. Thus far, the theory of variable exponent function spaces has seriously depended on the boundedness of the Hardy-Littlewood maximal operator. This restricts its applications in differential equations, approximation, and optimisation.

The aim of this Special Issue is to report developments in theory and applications of variable exponent function spaces, in particular, new variable exponent function spaces, the solvability of differential equations in variable exponent function spaces, the boundedness of operators in variable exponent function spaces, and approximations and optimisations in variable exponent function spaces. We also aim to provide a platform for researchers to promote, share, and discuss various problems in this area. We welcome both original research and review articles.

Potential topics include but are not limited to the following:

• Theory of variable exponent function spaces
• Differential equations in variable exponent function spaces
• Operators on variable exponent function spaces
• Approximations in variable exponent function spaces
• Optimisation in variable exponent function spaces
• Variable exponent function spaces of analytic functions