René Erlin Castillo - Böcker

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.

This book provides an introduction into the modern theory of classical harmonic analysis, dealing with Fourier analysis and the most elementary singular integral operators, the Hilbert transform and Riesz transforms. Ideal for self-study or a one semester course in Fourier analysis, included are detailed examples and exercises.

This book provides a comprehensive exploration of weighted function spaces, a fundamental topic in modern analysis. Beginning with the basics of weighted Lebesgue spaces, it systematically develops key properties such as duality, convexity, and interpolation. It delves into Muckenhoupt weights, Hardy and Carlson inequalities, and Calderón-Zygmund decompositions, highlighting their applications in harmonic analysis. With a structured and didactic approach, this work serves as an essential reference for researchers and graduate students in mathematical analysis, functional spaces, and related areas.

This book is devoted exclusively to Lebesgue spaces and their direct derived spaces. Unique in its sole dedication, this book explores Lebesgue spaces, distribution functions and nonincreasing rearrangement. Moreover, it also deals with weak, Lorentz and the more recent variable exponent and grand Lebesgue spaces with considerable detail to the proofs. The book also touches on basic harmonic analysis in the aforementioned spaces. An appendix is given at the end of the book giving it a self-contained character. This work is ideal for teachers, graduate students and researchers.