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 book deals with the constructive Weierstrassian approach to the theory of function
spaces and various applications. The first chapter is devoted to a detailed study of …

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 …

Operator theory and functional analysis have a long tradition, initially being guided by
problems from mathematical physics and applied mathematics. Much of the work in Banach …

The optimal Orlicz target space is exhibited for embeddings of fractional-order Orlicz–
Sobolev spaces in R n. An improved embedding with an Orlicz–Lorentz target space, which …

An embedding theorem for the Orlicz-Sobolev space W1, A 0 (G), G⊂ Rn, into a space of
Orlicz-Lorentz type is established for any given Young function A. Such a space is shown to …

The aim of this paper is to study Sobolev-type imbedding inequalities involving
rearrangement-invariant Banach function norms. We establish the equivalence of a Sobolev …

Until now, no book has systematically presented the recently developed concept of
envelopes in function spaces. Envelopes are relatively simple tools for the study of classical …

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 …