The purpose of this special issue is to present new developments in the theory of function spaces and their deep interconnections with approximation theory. In the last decades, several studies were carried out in this direction, with the aim to give applications in various fields of applied sciences, in particular, to signal analysis and image reconstruction. Also, the theory of integral transforms represents a powerful tool in describing basic function spaces, as Bernstein spaces, Paley-Wiener spaces, and their strict links with the theory of the sampling series. On the other hand, in recent years the problem of recovering discontinuous signals in function spaces, as the L^p spaces, Orlicz spaces, BV spaces and, more generally, modular function spaces, has received an increasing interest in image processing, employing approximation processes which use families of linear or nonlinear integral or discrete operators. These aspects give important motivations for theoretical studies of function spaces and approximation theory, with the aim to obtain new mathematical tools for real-life applications. Thus the main purpose of this special issue is to develop the fundamental links between function spaces, integral transforms, and approximation theory and to point out their various applications, by collecting papers containing both theoretical and applied results, as well as innovative mathematical models. The editors of this special issue invite research articles as well as review articles.

Potential topics include, but are not limited to:

• Approximation by linear and nonlinear operators
• Fourier, wavelet, and harmonic analysis methods in function spaces (Bernstein spaces, Paley-Wiener spaces, Sobolev spaces, Hardy spaces, Besov spaces, etc.)
• Univariate and multivariate sampling theory
• Applications to signal processing and image reconstructions, measure theory and spaces of measurable functions, and abstract integration processes in connections with function spaces