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Estas notas estan dirigidas fundamentalmente a los estudiantes de los ultimos anos de la carrera en Matematicas; asi como a quienes cursan estudios de Posgrado en las Universidades donde se imparte instruccion en la lengua castellana, como una guia de iniciacion a uno de los fascinantes temas del analisis armonico. Este material se ha ensamblado siguiendo un esquema de auto contencion, requiriendo solo del lector que este este familiarizado con el Teorema de la convergencia dominada, Lema de Fatou, Teorema de Fubini y rudimentos de analisis funcional."

Devoted to Lebesgue spaces and their direct derived spaces, this book explores Lebesgue spaces, distribution functions and nonincreasing rearrangement, as well as weak, Lorentz and recent variable exponent and grand Lebesgue spaces with considerable detail to the proofs. It also touches on basic harmonic analysis in the aforementioned spaces.

This work is solely dedicated to the study of both the one variable as well as the multidimensional Lorentz spaces covering the theory of Lebesgue type spaces invariant by rearrangement. The authors provide proofs in full detail for most theorems. The self-contained text is valuable for advanced students and researchers.