8 papers
Holmstedt's formula for the -functional: the limit case
Irshaad Ahmed, Alberto Fiorenza, Amiran Gogatishvili
We consider -interpolation spaces involving slowly varying functions, and derive necessary and sufficient conditions for a Holmstedt-type formula to be held in the limiting case…
Boundedness of Dunkl-Hausdorff operator in Lebesgue spaces
Sandhya Jain, Alberto Fiorenza, Pankaj Jain
In this paper, the -boundedness of the Dunkl-Hausdorff operator $\displaystyle H_{\al,ϕ} f(x)=\ent\frac{ |ϕ(t)|}{|t|^{2\al+2}}f\lf(\frac{x}{t}\rh) dt $ has been characte…
A short proof of local regularity of distributional solutions of Poisson's equation
Giovanni Di Fratta, Alberto Fiorenza
We prove a local regularity result for distributional solutions of the Poisson's equation with data. We use a very short argument based on Weyl's lemma and Riesz-Fréchet repr…
Gagliardo-Nirenberg Inequality for rearrangement-invariant Banach function spaces
Alberto Fiorenza, Maria Rosaria Formica, Tomas Roskovec +1
The classical Gagliardo-Nirenberg interpolation inequality is a well-known estimate which gives, in particular, an estimate for the Lebesgue norm of intermediate derivatives of fun…
Detailed proof of classical Gagliardo-Nirenberg interpolation inequality with historical remarks
Alberto Fiorenza, Maria Rosaria Formica, Tomáš Roskovec +1
A carefully written Nirenberg's proof of the well known Gagliardo-Nirenberg interpolation inequality for intermediate derivatives in seems, surprisingly, to be missi…
Interpolation of nonlinear positive or order preserving operators on Banach lattices
Ralph Chill, Alberto Fiorenza, Sebastian Krol
We study the relationship between exact interpolation spaces for positive, linear operators, for order preserving, Lipschitz continuous operators, and for positive Gagliardo-Peetre…