Function spaces are a central topic in mathematical analysis and in various other branches of mathematics. Some examples of function spaces include Lebesgue spaces, Herz spaces, sequence spaces, Lorentz spaces, Wiener amalgam spaces, Sobolev spaces, Orlicz spaces, Morrey spaces, Hölder-Zygmund spaces, Hardy spaces, Besov spaces, and Triebel-Lizorkin spaces.

The motivation for the increasing interest in function spaces is not only for theoretical purposes, but also because of their applications in a variety of fields, across harmonic analysis, physical sciences, and engineering. In particular, the concept of function spaces allows us to study, in a much wider perspective, partial differential equations (PDEs), boundary value problems, the boundedness of Hardy-Littlewood maximal functions, singular integral operators, pseudo-differential operators, and commutators. In order to deal with such problems, especially in PDEs, Hardy-type mathematical inequalities play a significant role, as in PDEs they are used to obtain a priori estimates and regularity results. They are also used in real interpolation theory, spectral theory, and geometric estimates.

The aim of this Special Issue is to present recent original research as well as review articles on the theory of function spaces, such as equivalent norms, embeddings, interpolation, and traces, as well as discrete, integral, and differential operators in function spaces and their applications in nonlinear partial differential equations. We encourage cooperation between researchers working in the theory of function spaces and applied mathematics.

Potential topics include but are not limited to the following:

• New perspectives in real/analytic function spaces
• Interpolation of function spaces
• Boundedness of sublinear operators on function spaces
• Interpolation inequalities and their applications
• Integral operators of Hardy type
• Weighted integral and discrete inequalities
• Nonlinear partial differential equations in function spaces