Fourier multipliers and spectral measures in Banach function spaces

作     者：de Pagter, Ben Ricker, Werner J. 

作者机构：Delft Univ Technol Delft Inst Appl Math Fac EEMCS NL-2600 GA Delft Netherlands Katholische Univ Eichstatt Ingolstadt Math Geogr Fak D-85072 Eichstatt Germany 

出 版 物：《POSITIVITY》 (Positivity)

年 卷 期：2009年第13卷第1期

页      面：225-241页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Fourier multiplier operators Banach function spaces 

摘      要：It is classical that amongst all spaces L-p (G), 1 = p = infinity, for G = R, Z or T say, only L-2 (G) ( that is, p = 2) has the property that every bounded Borel function on the dual group Gamma determines a bounded Fourier multiplier operator in L-2 (G). Stone s theorem asserts that there exists a regular, projection- valued measure (of operators on L-2 (G)), de. ned on the Borel sets of Gamma, with Fourier-Stieltjes transform equal to the group of translation operators on L-2 (G);this fails for every p not equal 2. We show that this special status of L-2 (G) amongst the spaces L-p (G), 1 = p = infinity, is actually more widespread;it continues to hold in a much larger class of Banach function spaces de. ned over G (relative to Haar measure).