Duv&#x27;an Cardona

Kernel estimates for the Weyl-Hörmander calculus, Weak (1,1) boundedness and other regularity properties

Duván Cardona, Julio Delgado, Manuel Martínez-Flores

We provide kernel estimates for pseudo-differential operators in the $S (m, g)$ Weyl-Hörmander calculus classes. These new results lead to boundedness theorems like the weak (1,1) ty…

Quasilinear equations with exponential growth for Hörmander $q$ -sub-Laplacians on stratified Lie groups

Jesus A. León Tordecilla, Duván Cardona

We prove the existence of positive weak solutions for a quasilinear equation with exponential nonlinearity on arbitrary stratified Lie groups for \emph{horizontal $q$ -Laplacians,}…

math.FA2026

On the differentiability of the Sobolev norm of $W^{k, 1} (M)$ on compact Riemannian manifolds

Duvan Cardona, Julio Delgado, Andres Felipe Muñoz-Tello

In this work we study the differentiability for the Sobolev norm of $W^{k, 1} (M)$ in the sense of Gâteaux , where $(M, g)$ is an arbitrary closed Riemannian manifold.

Kernel estimates and weak (1,1)-boundedness of pseudo-differential operators on compact Lie groups

Duván Cardona, Rafik Yeghoyan, Michael Ruzhansky

Given a compact Lie group $G$ and its unitary dual $G$ , we establish the weak (1,1) continuity for pseudo-differential operators in the global Hörmander classes of order…

Hyperbolic partial differential equations with complex characteristics on Fourier Lebesgue spaces

Duván Cardona, William Obeng-Denteh, Frederick Opoku

The aim of this paper is to establish well-posedness properties for hyperbolic PDEs on Fourier Lebesgue spaces. We consider hyperbolic operators with complex characteristics. Since…

Local smoothing estimates for bilinear Fourier integral operators

Duván Cardona

We formulate a local smoothing conjecture for bilinear Fourier integral operators in every dimension $d \geq 2,$ derived from the celebrated linear case due to Sogge, which we refer…

Boundedness of Fourier Integral Operators with complex phases on Fourier Lebesgue spaces

Duván Cardona, William Obeng-Denteh, Frederick Opoku

In this paper, we develop boundedness estimates for Fourier integral operators on Fourier Lebesgue spaces when the associated canonical relation is parametrised by a complex phase…

Estimates for pseudo-differential operators on the torus revisited. III

Duván Cardona, Manuel Alejandro Martínez

This paper finishes the goal of the authors started in two previous manuscripts dedicated to revisiting the continuity properties of toroidal pseudo-differential operators with sym…

math-ph2025

Riesz-means bounds for functional-difference operators for mirror curves

Duván Cardona

Let $ P $ and $ Q $ be the quantum-mechanical momentum and position operators on $ L^2(\R) $. Let $ζ > 0.$ We provide estimates for the {\it Riesz means} $ϰ (λ)$ associa…

Boundedness of pseudo-differential operators on the torus revisited. II

Duván Cardona, Manuel Alejandro Martínez

In this paper we continue our program of revisiting the new aspects about the boundedness properties of pseudo-differential operators on the torus. Here we prove $H^{p}$ - $L^{p}$ and $H…

Estimates for pseudo-differential operators on the torus revisited. I

Duván Cardona, Manuel Alejandro Martínez

In this paper we prove $L^{p}$ -estimates for Hörmander classes of pseudo-differential operators on the torus $T^{n}$ . The results are presented in the context of the global sy…

Nuclearity, Schatten-von Neumann classes, distribution of eigenvalues and $L^{p}$ - $L^{q}$ -boundedness of Fourier integral operators on compact manifolds

Duván Cardona, Julio Delgado, Michael Ruzhansky

We link Sogge's type $L^{p}$ -estimates for eigenfunctions of the Laplacian on compact manifolds with the problem of providing criteria for the $r$ -nuclearity of Fourier integral oper…

Well-posedness for a class of pseudo-differential hyperbolic equations on the torus

Duvan Cardona, Julio Delgado, Michael Ruzhansky

In this paper we establish the well-posedness of the Cauchy problem for a class of pseudo-differential hyperbolic equations on the torus. The class considered here includes a space…

On the Sobolev boundedness of vector fields on compact Riemannian manifolds

Duván Cardona, Alexandre Kirilov, Wagner A. A. de Moraes +1

We analyze the sharpness of the Sobolev order for left-invariant vector fields on compact Riemannian manifolds. Utilizing techniques from pseudo-differential operator theory and mi…

Pseudo-differential operators on Homogeneous vector bundles over compact homogeneous manifolds

Duván Cardona, Vishvesh Kumar, Michael Ruzhansky

In this work, we introduce a global theory of subelliptic pseudo-differential operators on arbitrary homogeneous vector bundles over orientable compact homogeneous manifolds. We wi…

The weak (1,1) boundedness of Fourier integral operators with complex phases

Duván Cardona, Michael Ruzhansky

Let $T$ be a Fourier integral operator of order $- (n - 1) /2$ associated with a canonical relation locally parametrised by a real-phase function. A fundamental result due to Seeger, S…

Anharmonic semigroups and applications to global well-posedness of nonlinear heat equations

Duván Cardona, Marianna Chatzakou, Julio Delgado +2

In this work we consider the semigroup $e^{- t A_{k, ℓ}^{γ}}$ for $γ > 0$ associated to an anharmonic oscillator of the form $A_{k, ℓ} = (- Δ)^{ℓ} + ∣ x ∣^{2 k}$ …

math.FA2024

$L^{2}$ -Maximal functions on graded Lie groups

Duván Cardona

Bourgain in his seminal paper [2] about the analysis of maximal functions associated to convex bodies, has estimated in a sharp way the $L^{2}$ -operator norm of the maximal function…

math.AP2024★ 1 cited

Estimates for the full maximal function on graded Lie groups

Duván Cardona

On $R^{n},$ a classical result due to Bourgain establishes the restricted weak $(\frac{n}{n - 1}, 1)$ inequality for the full maximal function $M_{F}^{d σ}$ associated to the sphe…

$L^{p}$ - $L^{q}$ estimates for subelliptic pseudo-differential operators on compact Lie groups

Duván Cardona, Julio Delgado, Vishvesh Kumar +1

We establish the $L^{p}$ - $L^{q}$ -boundedness of subelliptic pseudo-differential operators on a compact Lie group $G$ . Effectively, we deal with the $L^{p}$ - $L^{q}$ -bounds for operators in…

Global hypoellipticity of $G$ -invariant operators on homogeneous vector bundles

Duván Cardona, André Pedroso Kowacs

We establish necessary and sufficient conditions for the global hypoellipticity of $G$ -invariant operators on homogeneous vector bundles. These criteria are established in terms of…

math.AP2023★ 1 cited

$L^{p}$ - $L^{q}$ boundedness of pseudo-differential operators on graded Lie groups

Duván Cardona, Vishvesh Kumar, Michael Ruzhansky

In this paper we establish the $L^{p}$ - $L^{q}$ estimates for global pseudo-differential operators on graded Lie groups. We provide both necessary and sufficient conditions for the $L^p…

Degenerate Schrödinger equations with irregular potentials

Duván Cardona, Marianna Chatzakou, Julio Delgado +1

In this work we investigate a class of degenerate Schrödinger equations associated to degenerate elliptic operators with irregular potentials on $\Ran$ by introducing a suitable Hö…