arXiv subjects

Pablo L. De Nápoli

Publications and source records attributed to Pablo L. De Nápoli.

9 recordsLinked to original sources

arXiv2020

An Identity involving the Cyclotomic Polynomials

We present an elementary identity for the cyclotomic polynomials $Φ_n(X)$ which reflects a kind of multiplicative property of $Φ_n(X)$ as a function of $n$, and we explore its connections with the properties of other arithmetical functions. Important Note: In the first version of this article uploaded to the arXiv, it is said that this result seemed to be new. However, after that, I have learned that this identity (in Theorem 1.1) has previously appeared in Cheng, C. C. A., McKay, J. H., & Wang, S. S. S. (1995). Resultants of cyclotomic polynomials. Proceedings of the American Mathematical Society, 123(4), 1053-1059. (with a different proof).

math.NT↗

arXiv2016

Symmetry breaking for an elliptic equation involving the Fractional Laplacian

We study the symmetry breaking phenomenon for an elliptic equation involving the fractional Laplacian in a large ball. Our main tool is an extension of the Strauss radial lemma involving the fractional Laplacian, which might be of independent interest; and from which we derive compact embedding theorems for a Sobolev-type space of radial functions with power weights.

math.AP↗

arXiv2015

Weighted embedding theorems for radial Besov and Triebel-Lizorkin spaces

We study the continuity and compactness of embeddings for radial Besov and Triebel-Lizorkin spaces with weights in the Muckenhoupt class $A_\infty$. The main tool is a discretization in terms of an almost orthogonal wavelet expansion adapted to the radial situation.

math.CA↗

arXiv2013

Weighted convolution inequalities for radial functions

We obtain convolution inequalities in Lebesgue and Lorentz spaces with power weights when the functions involved are assumed to be radially symmetric. We also present applications of these results to inequalities for Riesz potentials of radial functions in weighted Lorentz spaces and embedding theorems for radial Besov spaces with power weights.

math.CA↗

arXiv2013

Lyapunov-type Inequalities for Partial Differential Equations

In this work we present a Lyapunov inequality for linear and quasilinear elliptic differential operators in $N-$dimensional domains $Ω$. We also consider singular and degenerate elliptic problems with $A_p$ coefficients involving the $p-$Laplace operator with zero Dirichlet boundary condition. As an application of the inequalities obtained, we derive lower bounds for the first eigenvalue of the $p-$Laplacian, and compare them with the usual ones in the literature.

math.AP↗

arXiv2012

$L^p$-boundedness properties for the maximal operators for semigroups associated with Bessel and Laguerre operators

In this paper we prove that the generalized (in the sense of Caffarelli and Calderón) maximal operators associated with heat semigroups for Bessel and Laguerre operators are weak type (1,1). Our results include other known ones and our proofs are simpler than the ones for the known special cases.

math.CA↗

arXiv2011

Multipliers of Laplace Transform Type for Laguerre and Hermite Expansions

We present a new criterion for the weighted $L^p-L^q$ boundedness of multiplier operators for Laguerre and Hermite expansions that arise from a Laplace-Stieltjes transform. As a special case, we recover known results on weighted estimates for Laguerre and Hermite fractional integrals with a unified and simpler approach.

math.CA↗

arXiv2010

Improved Caffarelli-Kohn-Nirenberg and trace inequalities for radial functions

We show that Caffarelli-Kohn-Nirenberg first order interpolation inequalities as well as weighted trace inequalities in $\mathbb{R}^n \times \mathbb{R}_+$ admit a better range of power weights if we restrict ourselves to the space of radially symmetric functions.

math.CA↗

arXiv2009

Multiple solutions for the $p-$laplace operator with critical growth

In this note we show the existence of at least three nontrivial solutions to the following quasilinear elliptic equation $-Δ_p u = |u|^{p^*-2}u + λf(x,u)$ in a smooth bounded domain $Ω$ of $\R^N$ with homogeneous Dirichlet boundary conditions on $\partialΩ$, where $p^*=Np/(N-p)$ is the critical Sobolev exponent and $Δ_p u =div(|\nabla u|^{p-2}\nabla u)$ is the $p-$laplacian. The proof is based on variational arguments and the classical concentrated compactness method.

math.AP↗