Functional and Harmonic Analysis
Description
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.
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René Erlín Castillo is Associated Profesor at Universidad Nacional de Colombia (Bogotá, Colombia). René Erlín Castillo obtained his PhD from Ohio University. He has been professor in Universidad de Oriente, Venezuela, Visiting Professor in Ohio University. His research, spread across around 90 papers, is done mainly in functional analysis, real analysis, complex analysis, harmonic analysis, operator theory, potential theory and partial Differential Equations. He has authored 6 books (3 in Spanish and 3 in English).
Héctor Camilo Chaparro Gutiérrez is a professor in the Faculty of Exact and Natural Sciences at the Universidad de Cartagena, Colombia. He earned his Ph.D. in Mathematics from the Universidad Nacional de Colombia in 2018, with a dissertation titled "Weighted composition operators on multidimensional Lorentz spaces and a glimpse on multipliers between bounded p-variation spaces," under the guidance of advisor René Erlin Castillo. His research interests include real analysis, harmonic analysis, and differential equations. In January 2023, Dr. Chaparro Gutiérrez was appointed as a full-time faculty member at the University of Cartagena. He has published 14 research articles and 1 book.
Julio C. Ramos-Fernández obtained his PhD in the Department of Mathematical Analysis at the Universidad de La Laguna, Tenerife, Spain. He began his academic career in 1994 and has since taught various mathematics courses, particularly in the field of Mathematical Analysis at the undergraduate, master's, and doctoral levels. He was a professor at the Universidad de Oriente, Venezuela (1994-2016) and currently works as a full-time faculty member at the Francisco José de Caldas District University in Bogotá, Colombia (since 2016). To date, he is the author of 70 research articles published in indexed journals, covering areas such as Real Analysis, Complex Analysis, Functional Analysis, Harmonic Analysis, Fourier Analysis, Operator Theory, Complex Function Theory, Geometric Function Theory, Differential Equations, Partial Differential Equations, Integral Equations, and Numerical Analysis. He is also the co-author of the book "Solutions for weakly coupled Quasilinear systems". He has been an invited speaker at 23 international events and has supervised 42 theses in mathematics: 29 at the undergraduate level, 11 at the master's level, and 4 at the doctoral level. Additionally, he serves as an editor and referee for several specialized mathematics journals.