From the reviews: "This book can be considered the third volume in an impressive series of books on theory of function spaces...but at the same time it is quite self-contained...The book is...extremely well-written, and reader-friendly, and it contains an enormous amount of deep and interesting material. It is strongly recommended to anybody interested in function spaces or in any of the related areas." -Mathematical Reviews "This book is to be considered as the continuation of the author's two monographs ['Theory of function spaces' [and] 'Theory of function spaces. II']; however, it is essentially self-contained and comprehensive...The author's other two monographs have already yielded deep influence to the development of the theory of function spaces. It is reasonable to expect that the present book will also push this field further. It should be extremely useful to graduate students and experts in the fields of fractal analysis, signal processing, numerics, harmonic analysis, PDE, real analysis, approximation theory and functional analysis." -Zentralblatt MATH "This book is the third part in a famous series of books on the theory of function spaces by the same author. ... After an intriguing historical survey in the introductory chapter, the book presents thorough discussions of typical building blocks as non-smooth atoms, quarks, wavelet bases, and wavelet frames. ... The current volume is an impressive and comprehensive account of the state of the art and can to a large extent be read independently ... ." (G. Hormann, Monatshefte fur Mathematik, Vol. 155 (2), October, 2008)

• How to Measure Smoothness.- Atoms and Pointwise Multipliers.- Wavelets.- Spaces on Lipschitz Domains, Wavelets and Sampling Numbers.- Anisotropic Function Spaces.- Weighted Function Spaces.- Fractal Analysis: Measures, Characteristics, Operators.- Function Spaces on Quasi-metric Spaces.- Function Spaces on Sets.

From the reviews: "This book can be considered the third volume in an impressive series of books on theory of function spaces...but at the same time it is quite self-contained...The book is...extremely well-written, and reader-friendly, and it contains an enormous amount of deep and interesting material. It is strongly recommended to anybody interested in function spaces or in any of the related areas." -Mathematical Reviews "This book is to be considered as the continuation of the author's two monographs ['Theory of function spaces' [and] 'Theory of function spaces. II']; however, it is essentially self-contained and comprehensive...The author's other two monographs have already yielded deep influence to the development of the theory of function spaces. It is reasonable to expect that the present book will also push this field further. It should be extremely useful to graduate students and experts in the fields of fractal analysis, signal processing, numerics, harmonic analysis, PDE, real analysis, approximation theory and functional analysis." -Zentralblatt MATH "This book is the third part in a famous series of books on the theory of function spaces by the same author. ... After an intriguing historical survey in the introductory chapter, the book presents thorough discussions of typical building blocks as non-smooth atoms, quarks, wavelet bases, and wavelet frames. ... The current volume is an impressive and comprehensive account of the state of the art and can to a large extent be read independently ... ." (G. Hormann, Monatshefte fur Mathematik, Vol. 155 (2), October, 2008)

• How to Measure Smoothness.- Atoms and Pointwise Multipliers.- Wavelets.- Spaces on Lipschitz Domains, Wavelets and Sampling Numbers.- Anisotropic Function Spaces.- Weighted Function Spaces.- Fractal Analysis: Measures, Characteristics, Operators.- Function Spaces on Quasi-metric Spaces.- Function Spaces on Sets.

From the reviews: "This book can be considered the third volume in an impressive series of books on theory of function spaces...but at the same time it is quite self-contained...The book is...extremely well-written, and reader-friendly, and it contains an enormous amount of deep and interesting material. It is strongly recommended to anybody interested in function spaces or in any of the related areas." -Mathematical Reviews "This book is to be considered as the continuation of the author's two monographs ['Theory of function spaces' [and] 'Theory of function spaces. II']; however, it is essentially self-contained and comprehensive...The author's other two monographs have already yielded deep influence to the development of the theory of function spaces. It is reasonable to expect that the present book will also push this field further. It should be extremely useful to graduate students and experts in the fields of fractal analysis, signal processing, numerics, harmonic analysis, PDE, real analysis, approximation theory and functional analysis." -Zentralblatt MATH "This book is the third part in a famous series of books on the theory of function spaces by the same author. ... After an intriguing historical survey in the introductory chapter, the book presents thorough discussions of typical building blocks as non-smooth atoms, quarks, wavelet bases, and wavelet frames. ... The current volume is an impressive and comprehensive account of the state of the art and can to a large extent be read independently ... ." (G. Hormann, Monatshefte fur Mathematik, Vol. 155 (2), October, 2008)

• How to Measure Smoothness.- Atoms and Pointwise Multipliers.- Wavelets.- Spaces on Lipschitz Domains, Wavelets and Sampling Numbers.- Anisotropic Function Spaces.- Weighted Function Spaces.- Fractal Analysis: Measures, Characteristics, Operators.- Function Spaces on Quasi-metric Spaces.- Function Spaces on Sets.