Theory of Function Spaces (Monographs in Mathematics) - ISBN:3764313811

Theory of Function Spaces (Monographs in Mathematics)

Date: 09 April 2011, 14:43

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Function spaces have a long history. They play an important part in both classical and modern mathematics. Space whose elements are continuous, or differentiate, or integrable functions are of interest for their own sake. They are also useful tools for the study of ordinary and partial differential equations (although they have some shortcomings for that purpose). Since the thirties more sophisticated function spaces have been used in the theory of partial differential equations, in the first place the Holder spaces and the Sobolev spaces. Later on (culminating in the fifties and in the sixties) many new spaces were created and investigated, e. g. Besov spaces (Lipschitz spaces. Bessel-potential spaces (Liouville spaces. Lebesgue spaces), Zygmund classes. Hardy spaces (real n-dimensional version1 and the space BMO. In the sixties and seventies, deep new tools were discovered: interpola: ion theory and the methods of the socalled ''hard analysis" (Fourier analysis, maximal inequalities, etc.). The main aim of this book is to present a unified theory of function spaces of the above-mentioned types from the standpoint of Fourier analysis.

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