Weighted extrapolation in Iwaniec–Sbordone spaces. Applications to integral operators and approximation theory

We prove extrapolation theorems in weighted Iwaniec–Sbordone spaces and apply them to one-weight inequalities for several integral operators of harmonic analysis. In addition, in weighted grand Lebesgue spaces, we establish Bernstein and Nikol'skii type inequalities and prove direct and inverse theorems on the approximation of functions.