The series is devoted to the publication of high-level monographs which cover the whole spectrum of current nonlinear analysis and applications in various fields, such as optimization, control theory, systems theory, mechanics, engineering, and other sciences. One of its main objectives is to make available to the professional community expositions of results and foundations of methods that play an important role in both the theory and applications of nonlinear analysis. Contributions which are on the borderline of nonlinear analysis and related fields and which stimulate further research at the crossroads of these areas are particularly welcome. Please submit book proposals to Jürgen Appell.

This is the first part of the second revised and extended edition of the well established book "Function Spaces" by Alois Kufner, Oldich John, and Svatopluk Fuík. Like the first edition this monograph is an introduction to function spaces defined in terms of differentiability and integrability classes. It provides a catalogue of various spaces and benefits as a handbook for those who use function spaces in their research or lecture courses. This first volume is devoted to the study of function spaces, based on intrinsic properties of a function such as its size, continuity, smoothness, various forms of a control over the mean oscillation, and so on. The second volume will be dedicated to the study of function spaces of Sobolev type, in which the key notion is the weak derivative of a function of several variables.

Auteur

Lubo Pick, Charles University, Prague, Czech Republic; Alois Kufner, The Academy of Sciences of the Czech Republic, Prague, Czech Republic; Old ich John, Charles University, Prague, Czech Republic; Svatopluk Füík .

Résumé

"Das Buch stellt dadurch eine nützliche Informationsquelle (ergänzt durch ein umfangreiches Literaturverzeichnis)dar, in einem nicht besonders übersichtlichen Teilgebiet."
V. Losert in: Monatsh Math 186 (2018), 561-564