Memoirs of the American Mathematical Society 2007; 97 pp; softcover Volume: 188 ISBN10: 0821839837 ISBN13: 9780821839836 List Price: US$66 Individual Members: US$39.60 Institutional Members: US$52.80 Order Code: MEMO/188/882
 The authors define axiomatically a large class of function (or distribution) spaces on \(N\)dimensional Euclidean space. The crucial property postulated is the validity of a vectorvalued maximal inequality of FeffermanStein type. The scales of Besov spaces (\(B\)spaces) and LizorkinTriebel spaces (\(F\)spaces), and as a consequence also Sobolev spaces, and Bessel potential spaces, are included as special cases. The main results of Chapter 1 characterize our spaces by means of local approximations, higher differences, and atomic representations. In Chapters 2 and 3 these results are applied to prove pointwise differentiability outside exceptional sets of zero capacity, an approximation property known as spectral synthesis, a generalization of Whitney's ideal theorem, and approximation theorems of Luzin (Lusin) type. Table of Contents  Introduction. Notation
 A class of function spaces
 Differentiability and spectral synthesis
 Luzin type theorems
 Appendix. Whitney's approximation theorem in \(L_p(\mathbf{R}^N), p>0\)
 Bibliography
