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 EMS Tracts in Mathematics 2013; 241 pp; hardcover Volume: 20 ISBN-10: 3-03719-123-6 ISBN-13: 978-3-03719-123-1 List Price: US$84 Member Price: US$67.20 Order Code: EMSTM/20 In this book a new approach is presented to exhibit relations between Sobolev spaces, Besov spaces, and Hölder-Zygmund spaces on the one hand and Morrey-Campanato spaces on the other. Morrey-Campanato spaces extend the notion of functions of bounded mean oscillation. These spaces play an important role in the theory of linear and nonlinear PDEs. Chapters 1-3 deal with local smoothness spaces in Euclidean $$n$$-space based on the Morrey-Campanato refinement of the Lebesgue spaces. The presented approach relies on wavelet decompositions. This is applied in Chapter 4 to Gagliardo-Nirenberg inequalities. Chapter 5 deals with linear and nonlinear heat equations in global and local function spaces. The obtained assertions about function spaces and nonlinear heat equations are used in Chapter 6 to study Navier-Stokes equations. The book is addressed to graduate students and mathematicians with a working knowledge of basic elements of (global) function spaces and an interest in applications to nonlinear PDEs with heat and Navier-Stokes equations as prototypes. A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society. Readership Graduate students and researchers interested in applications to nonlinear PDEs with heat and Navier-Stokes equations as prototypes. Table of Contents Global and local spaces Local spaces: Properties Morrey-Campanato spaces Gagliardo-Nirenberg inequalities Heat equations Navier-Stokes equations Bibliography Symbols Index