Add to ORKGLet Ω ⊂ Rn be of finite Lebesgue measure and 1 0 is embedded in the space L(p(Ω), which again is embedded in Lp(Ω). We present a way to find their norms which are based on the decreasing rearrangement. To get there, we define specific extrapolation and interpolation constructions and use them, alone and in combination, in order to characterise the spaces. Finally, we compare them to Lorentz-Zygmund spaces
Consider p : Ω → [1,+∞[, a measurable bounded function on a bounded set Ω with decreasing rearrange...
International audienceIn this paper we show, by elementary methods, that the quasinorms of the grand...
summary:This paper is an informal presentation of material from [28]–[34]. The monotone envelopes of...
We give equivalent, explicit expressions for the norms of the small and grand Lebesgue spaces, which...
The norm of the grand Lebesgue spaces is defined through the supremum of Lebesgue norms, balanced by...
A version of the Lebesgue differentiation theorem is offered, where the $L^p$ norm is replaced with ...
AbstractIt is proved in the case of Lebesgue measure space(R+,Σ,m) that for any p ϵ (0,1) the spaces...
In this paper, we show that the interpolation spaces between Grand, small or classical Lebesgue are ...
summary:In this paper, we are going to characterize the space ${\rm BMO}({\mathbb R}^n)$ through var...
We prove that if p> 1 and ψ:] 0 , p- 1 [→] 0 , ∞[is nondecreasing, then sup0<1ψ(p-11-logt)‖f∗‖...
We consider a generalized version of the small Lebesgue spaces, introduced by Fiorenza as the associ...
Yano’s extrapolation theorem dated back to 1951 establishes boundedness properties of a subadditive ...
If ψ: [0 , ℓ] → [0 , ∞[is absolutely continuous, nondecreasing, and such that ψ(ℓ) > ψ(0) , ψ(t) > 0...
We build a new class of Banach function spaces, whose function norm isρ(p[⋅],δ[⋅](f)=inff=∑k=1∞fk∑k...
Consider p : Ω → [1,+∞[, a measurable bounded function on a bounded set Ω with decreasing rearrange...
International audienceIn this paper we show, by elementary methods, that the quasinorms of the grand...
summary:This paper is an informal presentation of material from [28]–[34]. The monotone envelopes of...
We give equivalent, explicit expressions for the norms of the small and grand Lebesgue spaces, which...
The norm of the grand Lebesgue spaces is defined through the supremum of Lebesgue norms, balanced by...
A version of the Lebesgue differentiation theorem is offered, where the $L^p$ norm is replaced with ...
AbstractIt is proved in the case of Lebesgue measure space(R+,Σ,m) that for any p ϵ (0,1) the spaces...
In this paper, we show that the interpolation spaces between Grand, small or classical Lebesgue are ...
summary:In this paper, we are going to characterize the space ${\rm BMO}({\mathbb R}^n)$ through var...
We prove that if p> 1 and ψ:] 0 , p- 1 [→] 0 , ∞[is nondecreasing, then sup0<1ψ(p-11-logt)‖f∗‖...
We consider a generalized version of the small Lebesgue spaces, introduced by Fiorenza as the associ...
Yano’s extrapolation theorem dated back to 1951 establishes boundedness properties of a subadditive ...
If ψ: [0 , ℓ] → [0 , ∞[is absolutely continuous, nondecreasing, and such that ψ(ℓ) > ψ(0) , ψ(t) > 0...
We build a new class of Banach function spaces, whose function norm isρ(p[⋅],δ[⋅](f)=inff=∑k=1∞fk∑k...
Consider p : Ω → [1,+∞[, a measurable bounded function on a bounded set Ω with decreasing rearrange...
International audienceIn this paper we show, by elementary methods, that the quasinorms of the grand...
summary:This paper is an informal presentation of material from [28]–[34]. The monotone envelopes of...