Methods of Geometric Analysis in Extension and Trace Problems Volume 1

“Book under review is enormous in scope and contains
most of the old and current results on extension problems. Many of the theorems
appear here for the first time in book form. The book is self-contained, and
the detailed arguments make it accessible to a wide audience, especially
graduate students interested in getting into the subject. … It will become a
standard reference in the subject, and it deserves a spot in the library.” (Garving
K. Luli, Bulletin of the American Mathematical Society, Vol. 53 (1), January,
2016)

“The book is a unique (and therefore best) systematic presentation of the parts of analysis linked with the extension and trace problems. It is also a rich source of references and historical information on the topics under consideration. Undoubtedly, the book will influence significantly the research on the subject. The book is addressed at researchers, but it is also useful for lecturers as a source of supplementary material for standard courses of real and functional analysis.” (Victor Milman, Zentralblatt MATH, Vol. 1253, 2013)

“The two-volume monograph is divided into ten chapters, with five chapters in each volume. … the book successfully conveys the authors’ coherent vision for the subject, with the emphasis on linear extension operators, finiteness properties, and the treatment of extension via selection. It is certain to become a standard reference in the field.” (Leonid V. Kovalev, Mathematical Reviews, Issue 2012 j)

From the reviews:"The two-volume monograph is divided into ten chapters, with five chapters in each volume. ... the book successfully conveys the authors' coherent vision for the subject, with the emphasis on linear extension operators, finiteness properties, and the treatment of extension via selection. It is certain to become a standard reference in the field." (Leonid V. Kovalev, Mathematical Reviews, Issue 2012 j)"The book is a unique (and therefore best) systematic presentation of the parts of analysis linked with the extension and trace problems. It is also a rich source of references and historical information on the topics under consideration. Undoubtedly, the book will influence significantly the research on the subject. The book is addressed at researchers, but it is also useful for lecturers as a source of supplementary material for standard courses of real and functional analysis." (Victor Milman, Zentralblatt MATH, Vol. 1253, 2013)