Papers by Jairo Hernandez
We prove in this paper that a sequence M : Z → L(E) of bounded variation is a Fourier multiplier ... more We prove in this paper that a sequence M : Z → L(E) of bounded variation is a Fourier multiplier on the Besov space B p,q(T, E) for s ∈ R, 1 < p < ∞, 1 ≤ q ≤ ∞ and E a Banach space, if and only if E is a UMDspace. This extends the Theorem 4.2 in [3] to the n−dimensional case. As illustration of the applicability of this results we study the solvability of two abstract Cauchy problems with periodic boundary conditions.
emis.ams.org
In this work we consider a semilinear evolution problem which we pose as follows: Let Ω and Ωm be... more In this work we consider a semilinear evolution problem which we pose as follows: Let Ω and Ωm be two open bounded connected subsets of R2 with sufficiently smooth boundary ∂Ω and ∂Ωm so that Ωm ⊂⊂ Ω. Let Ωp := Ω\Ωm and Γ1 := ∂Ωm. We decompose ∂Ω in two ...
arXiv (Cornell University), Feb 22, 2022
We consider the equivalence of some norms in Sobolev spaces on bounded domains of R d and also in... more We consider the equivalence of some norms in Sobolev spaces on bounded domains of R d and also in Sobolev spaces on the boundaries of those domains.
Vector-valued function and distribution spaces on the torus
Mathematics, 2022
We consider Fourier multiplier systems on Rn with components belonging to the standard Hörmander ... more We consider Fourier multiplier systems on Rn with components belonging to the standard Hörmander class S1,0mRn, but with limited regularity. Using a notion of parameter-ellipticity with respect to a subsector Λ⊂C (introduced by Denk, Saal, and Seiler) we show the generation of both C∞ semigroups and analytic semigroups (in a particular case) on the Sobolev spaces WpkRn,Cq with k∈N0, 1≤p
In these notes, we present versions of trace theorems for Sobolev spaces over an interval in the ... more In these notes, we present versions of trace theorems for Sobolev spaces over an interval in the real line, and also a one-dimensional version of the well-known Poincare inequality.
We consider a beam-string-beam transmission problem, where two structurally damped or undamped be... more We consider a beam-string-beam transmission problem, where two structurally damped or undamped beams are coupled with a frictionally damped string by transmission conditions. We show that for this type of structure, the dissipation produced by the frictional part is strong enough to produce exponential decay of the solution, no matter how small is its size: for the exponential stability in the damped-damped-damped situation we use energy method and in the undamped-damped-undamped situation we use a frequency domain method from the semigroups theory, which combines a contradiction argument with the multiplier technique to carry out a special analysis for the resolvent. Additionally, we show that the solution first defined by the weak formulation, in fact have higher Sobolev space regularity.
Mathematical Methods in the Applied Sciences, 2021
In this paper we consider a transmission problem for a system of a thermoelastic plate with (or w... more In this paper we consider a transmission problem for a system of a thermoelastic plate with (or without) rotational inertia term coupled with a membrane with different variants of damping for the plate and/or the membrane. We prove well-posedness of the problem and higher regularity of the solution and study the asymptotic behaviour of the solution, depending on the damping and on the presence of the rotational term.
Journal of Mathematical Analysis and Applications, 2019
Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch ge... more Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence.
Journal of Fourier Analysis and Applications, 2015
We consider toroidal pseudodifferential operators with operator-valued symbols, their mapping pro... more We consider toroidal pseudodifferential operators with operator-valued symbols, their mapping properties and the generation of analytic semigroups on vector-valued Besov and Sobolev spaces. We show that a parabolic toroiodal pseudodifferential operator generates an analytic semigroup on the Besov space B s pq (T n , E) and on the Sobolev space W k p (T n , E), where E is an arbitrary Banach space, 1 ≤ p, q ≤ ∞, s ∈ R and k ∈ N0. For the proof of the Sobolev space result, we establish a uniform estimate on the kernel which is given as an infinite parameterdependent sum. An application to abstract non-autonomous periodic pseudodifferential Cauchy problems gives the existence and uniqueness of classical solutions for such problems.
Journal of Pseudo-Differential Operators and Applications, 2017
In this paper, we consider pseudodifferential operators on the torus with operator-valued symbols... more In this paper, we consider pseudodifferential operators on the torus with operator-valued symbols and prove continuity properties on vector-valued toroidal Besov spaces, without assumptions on the underlying Banach spaces. The symbols are of limited smoothness with respect to x and satisfy a finite number of estimates on the discrete derivatives. The proof of the main result is based on a description of the operator as a convolution operator with a kernel representation which is related to the dyadic decomposition appearing in the definition of the Besov space.
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Papers by Jairo Hernandez