An Introductory Course in Lebesgue Spaces

Introduces reader to recent topics in spaces of measurable functions Includes section of problems at the end of each chapter ​ Content allows for use with mixed-level classes Includes non-standard function spaces, viz. variable exponent Lebesgue spaces and grand Lebesgue spaces 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. Topics Abstract Harmonic Analysis Functional Analysis