Add to ORKGAbstract. We find new properties for the space R(X), intro-duced in [10] in the study of the best constant for the Hardy operator minus the identity. In particular we characterize when R(X) coincides with the minimal Lorentz space Λ(X). The condi-tion that R(X) 6 = {0} is also described in terms of the embedding (L1,∞∩L∞) ⊂ X. Finally, we also show the existence of a minimal RIBFS X among those for which R(X) 6 = {0} (which is the RIBFS envelope of the quasi-Banach space L1, ∞ ∩ L∞). 1
International audienceWe study in this chapter the main properties of Lorentz spaces L p,q (X) with ...
It is well known that the classical Sobolev embeddings may be improved within the framework of Loren...
This work is dealing with almost-compact embeddings of function spaces, in particular, the class of ...
AbstractAssociated to the class of restricted weak-type weights for the Hardy operator Rp, we find a...
AbstractSome problems in the theory of R-closed spaces are solved by showing that every regular spac...
summary:We show that for every $p\in (1,\infty )$ there exists a weight $w$ such that the Lorentz Ga...
Abstract. Let X be a quasi-Banach rearrangement invariant space and let T be a (ε, δ)-atomic operato...
summary:This paper is an informal presentation of material from [28]–[34]. The monotone envelopes of...
We investigate connections between Hardy's inequality in the whole space R-n and embedding inequalit...
Abstract. We provide a careful treatment of the weak Hardy spaces Hp,∞(Rn) for all indices 0 < p ...
Given non-negative measurable functions φ, ψ on Rn we study the high dimensional Hardy operator Hf(x...
AbstractWe find a new expression for the norm of a function in the weighted Loreritz space, with res...
summary:We study normability properties of classical Lorentz spaces. Given a certain general lattice...
We consider order and type properties of Marcinkiewicz and Lorentz function spaces. We show that if ...
A simple expression is presented that is equivalent to the norm of the Lpv --> Lqu embedding of t...
International audienceWe study in this chapter the main properties of Lorentz spaces L p,q (X) with ...
It is well known that the classical Sobolev embeddings may be improved within the framework of Loren...
This work is dealing with almost-compact embeddings of function spaces, in particular, the class of ...
AbstractAssociated to the class of restricted weak-type weights for the Hardy operator Rp, we find a...
AbstractSome problems in the theory of R-closed spaces are solved by showing that every regular spac...
summary:We show that for every $p\in (1,\infty )$ there exists a weight $w$ such that the Lorentz Ga...
Abstract. Let X be a quasi-Banach rearrangement invariant space and let T be a (ε, δ)-atomic operato...
summary:This paper is an informal presentation of material from [28]–[34]. The monotone envelopes of...
We investigate connections between Hardy's inequality in the whole space R-n and embedding inequalit...
Abstract. We provide a careful treatment of the weak Hardy spaces Hp,∞(Rn) for all indices 0 < p ...
Given non-negative measurable functions φ, ψ on Rn we study the high dimensional Hardy operator Hf(x...
AbstractWe find a new expression for the norm of a function in the weighted Loreritz space, with res...
summary:We study normability properties of classical Lorentz spaces. Given a certain general lattice...
We consider order and type properties of Marcinkiewicz and Lorentz function spaces. We show that if ...
A simple expression is presented that is equivalent to the norm of the Lpv --> Lqu embedding of t...
International audienceWe study in this chapter the main properties of Lorentz spaces L p,q (X) with ...
It is well known that the classical Sobolev embeddings may be improved within the framework of Loren...
This work is dealing with almost-compact embeddings of function spaces, in particular, the class of ...