36 citations · 234 across the 37 of their papers we have counts for
38 papers
Persistence of solutions to the Derivative Nonlinear Schrödinger equation in weighted Sobolev spaces
Alejandro J. Castro, Khumoyun Jabbarkhanov, Azamat Kassimbekov
In this paper we show the persistence property for solutions of the derivative nonlinear Schrödinger equation with initial data in weighted Sobolev spaces $H^{2}(\mathbb{R})\cap L^…
A note on the quartic generalized Korteweg-de Vries equation in weighted Sobolev spaces
Alejandro J. Castro, Amin Esfahani, Lyailya Zhapsarbayeva
In this paper we establish the persistence property for solutions of the quartic generalized Korteweg-de Vries equation with initial data in weighted Sobolev spaces $H^{s}(\mathbb{…
The Nonlinear Schrödinger-Airy equation in weighted Sobolev spaces
Alejandro J. Castro, Khumoyun Jabbarkhanov, Lyailya Zhapsarbayeva
We study the persistence property of the solution for the nonlinear Schrödinger-Airy equation with initial data in the weighted Sobolev space $H^{1/4}(\mathbb{R})\cap L^2(|x|^{2m}d…
Variation operators for semigroups associated with Fourier-Bessel expansions
Jorge J. Betancor, Alejandro J. Castro, Marta De León-Contreras
In this paper we establish -boundedness properties for variation operators defined by semigroups associated with Fourier-Bessel expansions.
The Hardy-Littlewood property and maximal operators associated with the inverse Gauss measure
Jorge J. Betancor, Alejandro J. Castro, Marta De León-Contreras
In this paper we characterize the Banach lattices with the Hardy-Littlewood property by using maximal operators defined by semigroups of operators associated with the inverse Gauss…
Regularity of Fourier integral operators with amplitudes in general Hörmander classes
Alejandro J. Castro, Anders Israelsson, Wolfgang Staubach
We prove the global -boundedness of Fourier integral operators that model the parametrices for hyperbolic partial differential equations, with amplitudes in classical Hörmande…
Regularity properties of Schrödinger integral operators and general oscillatory integrals
Alejandro J. Castro, Anders Israelsson, Wolfgang Staubach +1
We introduce the notion of Schrödinger integral operators and prove sharp local and global regularity results for these (including propagators for the quantum mechanical harmonic o…
Global well-posedness for the nonlinear wave equation in analytic Gevrey spaces
Daniel Oliveira da Silva, Alejandro J. Castro
We obtain an asymptotic rate of decay for the radius of spatial analyticity of solutions to the nonlinear wave equation with initial data in the analytic Gevrey spaces.
Riesz transforms, Cauchy-Riemann systems and amalgam Hardy spaces
Al-Tarazi Assaubay, Jorge J. Betancor, Alejandro J. Castro +1
In this paper we study Hardy spaces , , modeled over amalgam spaces . We characterize $\mathcal{H}^{p,q}(…
BMO functions and Balayage of Carleson measures in the Bessel setting
Víctor Almeida, Jorge J. Betancor, Alejandro J. Castro +2
By we denote the space consisting of all those odd and bounded mean oscillation functions on R. In this paper we characterize the functions in with bounded su…
Transference of local to global maximal estimates for dispersive partial differential equations
Alejandro J. Castro, Salvador Rodríguez-López, Wolfgang Staubach
In this paper we give an elementary proof for transference of local to global maximal estimates for dispersive PDEs. This is done by transferring local estimates for certain…
Variable exponent Hardy spaces associated with discrete Laplacians on graphs
Víctor Almeida, Jorge J. Betancor, Alejandro J. Castro +1
In this paper we develop the theory of variable exponent Hardy spaces associated with discrete Laplacians on infinite graphs. Our Hardy spaces are defined by square integrals, atom…
Homogenization of a parabolic Dirichlet problem by a method of Dahlberg
Alejandro J. Castro, Martin Strömqvist
Consider the linear parabolic operator in divergence form We employ a method of Dahlberg to show that the Dirich…
Oscillation of generalized differences of Hölder and Zygmund functions
Alejandro J. Castro, José G. Llorente, Artur Nicolau
In this paper we analyze the oscillation of functions having derivatives in the Hölder or Zygmund class in terms of generalized differences and prove that its growth is governed by…
Discrete harmonic analysis associated with ultraspherical expansions
Jorge J. Betancor, Alejandro J. Castro, Juan C. Fariña +1
We study discrete harmonic analysis associated with ultraspherical orthogonal functions. We establish weighted l^p-boundedness properties of maximal operators and Littlewood-Paley…
Boundedness of single layer potentials associated to divergence form parabolic equations with complex coefficients
Alejandro J. Castro, Kaj Nyström, Olow Sande
We consider parabolic operators of the form $$\partial_t+\mathcal{L},\ \mathcal{L}:=-\mbox{div}\, A(X,t)\nabla,$$ in $\mathbb R_+^{n+2}:=\{(X,t)=(x,x_{n+1},t)\in \mathbb R^{n}\time…
Solvability of the Dirichlet, Neumann and the regularity problems for parabolic equations with Hölder continuous coefficients
Alejandro J. Castro, Salvador Rodríguez-López, Wolfgang Staubach
We establish the -solvability of Dirichlet, Neumann and regularity problems for divergence-form heat (or diffusion) equations with Hölder-continuous diffusion coefficients, on…
Variable exponent Sobolev spaces associated with Jacobi expansions
V. Almeida, J. J. Betancor, A. J. Castro +2
In this paper we define variable exponent Sobolev spaces associated with Jacobi expansions. We prove that our generalized Sobolev spaces can be characterized as variable exponent p…
Solutions of Weinstein equations representable by Bessel Poisson integrals of BMO functions
Jorge J. Betancor, Alejandro J. Castro, Juan C. Fariña +1
We consider the Weinstein type equation on , where , with . In…
Bounds for partial derivatives: necessity of UMD and sharp constants
Alejandro J. Castro, Tuomas P. Hytönen
We prove the necessity of the UMD condition, with a quantitative estimate of the UMD constant, for any inequality in a family of bounds between different partial derivatives…
Riesz-Jacobi transforms as principal value integrals
Alejandro J. Castro, Adam Nowak, Tomasz Z. Szarek
We establish an integral representation for the Riesz transforms naturally associated with classical Jacobi expansions. We prove that the Riesz-Jacobi transforms of odd orders expr…
Conical square functions associated with Bessel, Laguerre and Schrödinger operators in UMD Banach spaces
Jorge J. Betancor, Alejandro J. Castro, Juan C. Fariña +1
In this paper we consider conical square functions in the Bessel, Laguerre and Schrödinger settings where the functions take values in UMD Banach spaces. Following a recent paper o…
On fundamental harmonic analysis operators in certain Dunkl and Bessel settings
Alejandro J. Castro, Tomasz Z. Szarek
We consider several harmonic analysis operators in the multi-dimensional context of the Dunkl Laplacian with the underlying group of reflections isomorphic to (als…
Riesz transforms and multipliers for the Bessel-Grushin operator
Víctor Almeida, Jorge J. Betancor, Alejandro J. Castro +1
We establish that the spectral multiplier associated to the differential operator $$ G_α=- Δ_x +\sum_{j=1}^m{{α_j^2-1/4}\over{x_j^2}}-|x|^2 Δ_y \; \text{on} (0,\inf…