\(L_p\)-boundedness of the Laplace transform

René Erlín Castillo; Héctor Camilo Chaparro; Julio César Ramos-Fernández

doi:10.56754/0719-0646.2602.359

Authors

René Erlín Castillo Departamento de Matemáticas, Universidad Nacional de Colombia, Bogotá, Colombia. https://orcid.org/0000-0003-1113-5827
Héctor Camilo Chaparro Programa de Matemáticas, Universidad de Cartagena, Cartagena de Indias, Colombia. https://orcid.org/0000-0002-0723-8199
Julio César Ramos-Fernández Facultad de Ciencias Matemáticas y Naturales, Universidad Distrital Francisco José de Caldas, Bogotá, Colombia. https://orcid.org/0000-0002-7329-5263

DOI:

https://doi.org/10.56754/0719-0646.2602.359

Keywords:

Laplace transform, Integral transform, \(L_p\)-strong boundedness

Abstract

In this paper, we discuss about the boundedness of the Laplace transform \(\mathcal{L}: L_p([0,\infty))\rightarrow L_p(A)\) (\(p\geq1\)) for the cases \(A=[0, \infty)\), \(A=[1, \infty)\) and \(A=[0, 1]\). We also provide examples for the cases where \(\mathcal{L}\) is unbounded.

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