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AuthorTriebel, Hans. author
TitleTheory of Function Spaces [electronic resource] / by Hans Triebel
ImprintBasel : Springer Basel, 1983
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Descript IV, 281 p. online resource


The book deals with the two scales Bsp,q and Fsp,q of spaces of distributions, where โ{128}{145}โ{136}{158}<s<โ{136}{158} and 0<p,qโ{137}คโ{136}{158}, which include many classical and modern spaces, such as Hรถlder spaces, Zygmund classes, Sobolev spaces, Besov spaces, Bessel-potential spaces, Hardy spaces and spaces of BMO-type. It is the main aim of this book to give a unified treatment of the corresponding spaces on the Euclidean n-space Rn in the framework of Fourier analysis, which is based on the technique of maximal functions, Fourier multipliers and interpolation assertions. These topics are treated in Chapter 2, which is the heart of the book. Chapter 3 deals with corresponding spaces on smooth bounded domains in Rn. These results are applied in Chapter 4 in order to study general boundary value problems for regular elliptic differential operators in the above spaces. Shorter Chapters (1 and 5-10) are concerned with: Entire analytic functions, ultra-distributions, weighted spaces, periodic spaces, degenerate elliptic differential equations. ย ------ย  Reviews ย It is written in a concise but well readable style. (โ{128}ฆ) This book can be best recommended to researchers and advanced students working on functional analysis or functional analytic methods for partial differential operators or equations. - Zentralblatt MATH ย The noteworthy new items in the book are: the use of maximal functions, treatment of BMO spaces, treatment of Beurling ultradistributions as well as addition of new results, too numerous to mention, obtained within the last 7 years or so. - Mathematical Reviews


Spaces of Entire Analytic Functions -- Function Spaces on Rn -- Function Spaces on Domains -- Regular Elliptic Differential Equations -- Homogeneous Function Spaces -- Ultra-Distributions and Weighted Spaces of Entire Analytic Functions -- Weighted Function Spaces on Rn -- Weighted Function Spaces on Domains and Degenerate Elliptic Differential Equations -- Periodic Function Spaces -- Further Types of Function Spaces

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