We study the Hardy inequality and derive the maximal theorem of Hardy and Littlewood in
the context of grand Lebesgue spaces, considered when the underlying measure space is …

In this paper, we show that the interpolation spaces between Grand, small or classical
Lebesgue are so called Lorentz–Zygmund spaces or more generally G Γ-spaces. As a direct …

This paper is essentially a survey on grand and small Lebesgue spaces, which are
rearrangement-invariant Banach function spaces of interest not only from the point of view of …

We introduce grand Lebesgue spaces on open sets Ω of infinite measure in Rn, controlling
the integrability of| f (x)| p− ε at infinity by means of a weight (depending also on ε); in …

Let 1< p<∞. Given Ω⊂ Rn a measurable set of finite Lebesgue measure, the norm of the
grand Lebesgue spaces Lp)(Ω) is given by In this paper we consider the norm [Formula: see …

A brief survey of results on the characterization of the spaces associated with given classes
of function spaces is presented. It is shown that the situation differs in general for ideal and …

Some regularity results in small Lebesgue spaces for the weak or the very weak solution of
the linear equation -Δu=f are given, improving all the previous results obtained in the usual …

We compute the K-functional related to some couple of spaces as small or classical
Lebesgue space or Lorentz-Marcinkiewicz spaces completing the results of [11]. This …

We define and study the grand Morrey spaces and the grand Hardy–Morrey spaces on
Euclidean space. We also introduce the small block space and study the duality between the …

In this note we introduce grand grand Morrey spaces, in the spirit of the grand Lebesgue
spaces. We prove a kind of reduction lemma which is applicable to a variety of operators to …