Browsing Analysis of Partial Differential Equations (APDE) by Title
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Maximal estimates for a generalized spherical mean Radon transform acting on radial functions
(Annali de Matematica Pura et Applicata, 2020)We study a generalized spherical means operator, viz.\ generalized spherical mean Radon transform, acting on radial functions. As the main results, we find conditions for the associated maximal operator and its local ... 
Meanfield dynamics of the spinmagnetization coupling in ferromagnetic materials: Application to currentdriven domain wall motions
(IEEE Transactions on Magnetics, 20151231)In this paper, we present a meanfield model of the spinmagnetization coupling in ferromagnetic materials. The model includes nonisotropic diffusion for spin dynamics, which is crucial in capturing strong spinmagnetization ... 
Minimizers of a Landaude Gennes energy with a subquadratic elastic energy
(Archive for Rational Mechanics and Analysis, 2019)We study a modified Landaude Gennes model for nematic liq uid crystals, where the elastic term is assumed to be of subquadratic growth in the gradient. We analyze the behaviour of global minimizers in two and threedimensional ... 
Mixed norm estimates for the Cesàro means associated with DunklHermite expansions
(Transactions of the American Mathematical Society, 2017)Our main goal in this article is to study mixed norm estimates for the Cesàro means associated with DunklHermite expansions on $\mathbb{R}^d$. These expansions arise when one considers the DunklHermite operator ... 
Mixed weak type estimates: Examples and counterexamples related to a problem of E. Sawyer
(Colloquium Mathematicum, 20160101)In this paper we study mixed weighted weaktype inequal ities for families of functions, which can be applied to study classic operators in harmonic analysis. Our main theorem extends the key result from [CMP2]. 
Modeling cardiac structural heterogeneity via spacefractional differential equations
(Computational and Mathematical Biomedical Engineering (CMBE2017) Proceedings, 2017)We discuss here the use of nonlocal models in space and fractional order operators in the characterisation of structural complexity and the modeling of propagation in heterogeneous biological tissues. In the specific, we ... 
Models for damped water waves
(SIAM Journal of Applied Mathematics, 2019)In this paper we derive some new weakly nonlinear asymptotic models describing viscous waves in deep water with or without surface tension effects. These asymptotic models take into account several different dissipative ... 
Monotonicity and convexity of the ratios of the first kind modified Bessel functions and applications
(Mathematical Inequalities & Applications, 20170718)Let $I_{v}\left( x\right) $ be modified Bessel functions of the first kind. We prove the monotonicity property of the function $x\mapsto I_{u}\left( x\right) I_{v}\left( x\right) /I_{\left( u+v\right) /2}\left( x\right) ... 
New bounds for bilinear CalderónZygmund operators and applications
(Revista Matemática Iberoamericana, 20161125)In this work we extend Lacey’s domination theorem to prove the pointwise control of bilinear Calderón–Zygmund operators with Dini–continuous kernel by sparse operators. The precise bounds are carefully tracked following ... 
Nonlocal discrete diffusion equations and the fractional discrete Laplacian, regularity and applications
(Adv. Math., 2018)The analysis of nonlocal discrete equations driven by fractional powers of the discrete Laplacian on a mesh of size $h>0$ \[ (\Delta_h)^su=f, \] for $u,f:\Z_h\to\R$, $0<s<1$, is performed. The pointwise nonlocal ... 
A note on generalized Poincarétype inequalities with applications to weighted improved Poincarétype inequalities
(2020)The main result of this paper supports a conjecture by C. P\'erez and E. Rela about the properties of the weight appearing in their recent selfimproving result of generalized inequalities of Poincar\'etype in the Euclidean ... 
A note on the offdiagonal MuckenhouptWheeden conjecture
(WSPC Proceedings, 20160701)We obtain the offdiagonal MuckenhouptWheeden conjecture for CalderónZygmund operators. Namely, given $1 < p < q < \infty$ and a pair of weights $(u; v)$, if the HardyLittlewood maximal function satisfies the following ... 
On a hyperbolic system arising in liquid crystal modelling
(Journal of Hyperbolic Differential Equations, 201711)We consider a model of liquid crystals, based on a nonlinear hyperbolic system of differential equations, that represents an inviscid version of the model proposed by Qian and Sheng. A new concept of dissipative solution ... 
On Bloom type estimates for iterated commutators of fractional integrals
(Indiana University Mathematics Journal, 201804)In this paper we provide quantitative Bloom type estimates for iterated commutators of fractional integrals improving and extending results from [15]. We give new proofs for those inequalities relying upon a new sparse ... 
On extension problem, trace hardy and Hardy’s inequalities for some fractional Laplacians
(Communications on pure and applied analysis, 201909)We obtain generalised trace Hardy inequalities for fractional powers of general operators given by sums of squares of vector fields. Such inequalities are derived by means of particular solutions of an extended equation ... 
On pointwise and weighted estimates for commutators of CalderónZygmund operators
(Advances in Mathematics, 2017)In recent years, it has been well understood that a CalderónZygmund operator T is pointwise controlled by a finite number of dyadic operators of a very simple structure (called the sparse operators). We obtain a similar ... 
On sums involving Fourier coefficients of Maass forms for SL(3,Z)
(20160910)We derive a truncated Voronoi identity for rationally additively twisted sums of Fourier coefficients of Maass forms for SL(3,Z), and as an application obtain a pointwise estimate and a second moment estimate for the sums ... 
On the absolute divergence of Fourier series in the infinite dimensional torus
(Colloquium Mathematicum, 20190322)In this note we present some simple counterexamples, based on quadratic forms in infinitely many variables, showing that the implication $f\in C^{(\infty}(\mathbb{T}^\omega)\Longrightarrow\sum_{\bar{p}\in\mathbb{Z}^\inf ... 
On the bound states of Schrödinger operators with $\delta$interactions on conical surfaces
(Communications in Partial Differential Equations, 20160630)In dimension greater than or equal to three, we investigate the spectrum of a Schrödinger operator with a $\delta$interaction supported on a cone whose cross section is the sphere of codimension two. After decomposing ... 
On the controllability of Partial Differential Equations involving nonlocal terms and singular potentials
(20161212)In this thesis, we investigate controllability and observability properties of Partial Differential Equations describing various phenomena appearing in several fields of the applied sciences such as elasticity theory, ...