20 citations · 20 across the 11 of their papers we have counts for
12 papers
Quasilinear P.D.Es, Interpolation spaces and Hölderian mappings
Irshaad Ahmed, Alberto Fiorenza, Maria Rosaria Formica +3
As in the work of Tartar ( Tartar L. Interpolation non linéaire et régularité, 9, Journal of Functional Analysis, (1972), 469-489) we developed here some new results on non linear…
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…
On symmetry of energy minimizing harmonic-type maps on cylindrical surfaces
Giovanni Di Fratta, Alberto Fiorenza, Valeriy Slastikov
The paper concerns the analysis of global minimizers of a Dirichlet-type energy functional in the class of -valued maps defined in cylindrical surfaces. The model nat…
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…
Modular inequalities for the maximal operator in variable Lebesgue spaces
David Cruz-Uribe, Giovanni Di Fratta, Alberto Fiorenza
A now classical result in the theory of variable Lebesgue spaces due to Lerner [A. K. Lerner, On modular inequalities in variable spaces, Archiv der Math. 85 (2005), no. 6, 5…
Embeddings between grand, small and variable Lebesgue spaces
David Cruz-Uribe, Alberto Fiorenza, Oscar Guzman
We give conditions on the exponent function that imply the existence of embeddings between grand, small and variable Lebesgue spaces. We construct examples to show that…
The action of Volterra integral operators with highly singular kernels on Hölder continuous, Lebesgue and Sobolev functions
Raffaele Carlone, Alberto Fiorenza, Lorenzo Tentarelli
For kernels which are positive and integrable we show that the operator on a finite time interval enjoys a regularizing effect when applie…
Some estimates for imaginary powers of the Laplace operator in variable Lebesgue spaces and applications
Alberto Fiorenza, Amiran Gogatishvili, Tengiz Kopaliani
In this paper we study some estimates of norms in variable exponent Lebesgue spaces for a singular integral operators that are imaginary powers of the Laplace operator in . U…