An Introductory Course in Lebesgue Spaces

Rene Erlin Castillo, Humberto Rafeiro (Autoren)

Buch | Hardcover

XII, 461 Seiten

2016 | 1st ed. 2016
Springer International Publishing (Verlag)
978-3-319-30032-0 (ISBN)

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lt;p>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.

René Erlín Castillo obtained his PhD from Ohio University. He has been professor in Universidad de Oriente, Venezuela, Visiting Professor in Ohio University and nowadays he is a professor in the Universidad Nacional de Colombia. His research, spread across around 50 papers, is done mainly in functional analysis, real analysis, complex analysis, harmonic analysis, operator theory, potential theory and partial Differential Equations. He has authored a book and a textbook both in Spanish. Humberto Rafeiro received his PhD from Algarve University, Portugal and did postdoctoral work in the research group Centro de Análise Funcional e Aplicações in the Instituto Superior Técnico, Universidade de Lisboa, Portugal. Nowadays he is a professor in the Pontifical Universidad Javeriana. His research interests range from harmonic analysis, function spaces, operator theory in non-standard function spaces, potential type operators, hypersingular integrals and fractional calculus, having published near 40 papers on these subjects. He has co-authored a textbook in Spanish.

Convex Functions and Inequalities.- Lebesgue Sequence Spaces.- Lebesgue Spaces.- Distribution Function and Non-Increasing Rearrangement.- Weak Lebesgue Spaces.- Lorentz Spaces.- Non-Standard Lebesgue Spaces.- Interpolation of Operators.- Maximal Operator.- Integral Operators.- Convolution and Potentials.- Appendices.

"The book under review is dedicated solely to Lebesgue spaces and their direct derivatives ... . The book may be recommended to graduate students and non-specialists in the area of function spaces. ... Each chapter is concluded with an extensive list of problems and short bibliographic notes. ... The book ends with a list of 86 references and with symbol and subject indices." (Alexei Yu. Karlovich, zbMATH 1352.46003, 2017)

Erscheinungsdatum	08.10.2016
Reihe/Serie	CMS Books in Mathematics
Zusatzinfo	XII, 461 p. 14 illus.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Schlagworte	Abstract harmonic analysis • Convex Functions • Functional Analysis • grand Lebesgue spaces • Interpolation of operators • Lebesgue Spaces • Lorentz spaces • mathematics and statistics • maximal operator • variable exponent Lebesgue spaces
ISBN-10	3-319-30032-6 / 3319300326
ISBN-13	978-3-319-30032-0 / 9783319300320
Zustand	Neuware