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 …

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 introduce the martingale Hardy–Lorentz–Karamata spaces. The atomic decompositions
of these martingale function spaces are established. The dual spaces are identified and …

In this paper, the generalized BMO martingale spaces are introduced as the dual spaces of
martingale Hardy–Lorentz–Karamata spaces, which completes the very recent result [Quart …

In this paper, we introduce a new class of function spaces, which unify and generalize
Lorentz-Karamata spaces, variable Lorentz spaces and other several classical function …

We introduce the Littlewood-Paley spaces in which the Lebesgue spaces, the Hardy spaces,
the Orlicz spaces, the Lorentz-Karamata spaces, the r.-i. quasi-Banach function spaces and …

We study continuity envelopes in spaces of generalised smoothness Bpq (s, Ψ) and Fpq (s,
Ψ) and give some new characterisations for spaces Bpq (s, Ψ). The results are applied to …

Abstract Given E 0, E 1, E, F rearrangement invariant spaces, a, b, b 0, b 1 slowly varying
functions and 0≤ θ 0< θ 1≤ 1, we characterize the interpolation spaces (X‾ θ 0, b 0, E 0, a …

We establish conditions under which K‐spaces in the limiting real interpolation involving
slowly varying functions can be described by means of J‐spaces and we also solve the …

Let 0< q≤∞, b be a slowly varying function and Φ:[0,∞)⟶[0,∞) be an increasing function
with Φ (0)= 0 and lim r→∞ Φ (r)=∞. In this paper, we introduce a new class of function …