Vector-valued function and distribution spaces on the torus (PDF)

This book contains details of the properties that satisfy certain function spaces and vector-valued distributions defined in the n-dimensional torus.
In particular, the text deals with an introductory study of toroidal Besov spaces, which make their appearance in many applications to partial equations differential (PDEs).

The book is born out of the motivation left by the research project titled Operadores Pseudodiferenciales Banach vector-valuados en el toro ndimensional (financed by Colciencias 2013-2015, code 121556933488, which included the products [9], [7] and [14], among others, and which had the collaboration of Robert Denk and his research group attached to the Department of Mathematics and Statistics at the University of Konstanz, Germany). At that time, in a literary search, we found several well-known and excellent texts on the subject of Besovs toroidal spaces (see [6], [30] and [32]), but in contrast to these texts, here we have included the vector valued case on the n-dimensional torus Tn (n = 1) and an effort is made to present clearly and in detail everything that corresponds to the torus. Our goal is to provide the reader with a more pleasant introduction to this subject, for example, in the study of harmonic analysis and PDEs with periodic conditions. Concerning Rn we do not discuss many details because that would lead to many pages of explanations, which is outside of our stated intention, and a significant amount of literature on the subject already exists.

We expect that this book will be of great interest to undergraduate and graduate students in mathematics, as well as to mathematical researchers
who would like an introduction to the previously mentioned topic.

Este libro contiene parte de los resultados de un proyecto de investigación financiado por Colciencias y ejecutado por el Grupo de Investigación en Matemáticas Uninorte, y contiene detalles de propiedades que son satisfechas por ciertos espacios de funciones y distribuciones con valores vectoriales definidas en el Toro n-dimensional. En particular, el texto aborda un estudio introductorio de los espacios de Besov toroidales, los cuales aparecen en muchas aplicaciones a las ecuaciones diferenciales parciales con condiciones periódicas y en el análisis armónico.

Este trabajo puede ser muy útil para estudiantes de pregrado y posgrado en matemáticas, así como para investigadores interesados en los temas mencionados anteriormente.