Classical Sobolev spaces, based on Lebesgue spaces on an underlying domain with
smooth boundary, are not only of considerable intrinsic interest but have for many years …

This is the first part of the second revised and extended edition of the well established book"
Function Spaces" by Alois Kufner, Oldřich John, and Svatopluk Fučík. Like the first edition …

Let m and n be positive integers with n⩾ 2 and 1⩽ m⩽ n− 1. We study rearrangement-
invariant quasinorms ϱR and ϱD on functions f:(0, 1)→ R such that to each bounded …

We study generalized Lorentz–Zygmund spaces with broken logarithmic functions. We
derive necessary and sufficient conditions for embeddings between them. We give a …

We present an extrapolation theory that allows us to obtain, from weighted Lp inequalities on
pairs of functions for p fixed and all A∞ weights, estimates for the same pairs on very …

Let X be a rearrangement-invariant Banach function space on R n and let V 1 X be the
Sobolev space of functions whose gradient belongs to X. We give necessary and sufficient …

We present reiteration formulae with limiting values θ= 0 and θ= 1 for a real interpolation
method involving slowly varying functions. Applications to the Lorentz–Karamata spaces, the …

We present a real interpolation method involving broken-logarithmic functors. We obtain a
variety of interpolation theorems for quasilinear operators on quasi-Banach spaces …

Optimal higher-order Sobolev type embeddings are shown to follow via isoperimetric
inequalities. This establishes a higher-order analogue of a well-known link between first …

We present embedding theorems for certain logarithmic Bessel potential spaces modelled
upon generalized Lorentz–Zygmund spaces and clarify the role of the logarithmic terms …