by **
W. Farkas**

**Preprint series:**
98-34, Analysis

**The paper is published:**
Math. Nachr., 209, 83-113, 2000

**MSC:**- 46E35 Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
- 42B25 Maximal functions, Littlewood-Paley theory

**Abstract:** This work deals with decompositions in anisotropic function spaces. Defining anisotropic atoms as smooth building blocks which are the counterpart of the atoms from the works of M. Frazier and B. Jawerth, it is shown that the study of anisotropic function spaces can be done with the help of some sequence spaces in a similar way as it is done in the isotropic case. It is also shown that the subatomic decomposition theorem for isotropic function spaces, recently proved by H. Triebel, can be extended to the anisotropic case if the mean smoothness parameter is sufficiently large.

**Keywords:** *anisotropic function space, atomic decomposition, subatomic decomposition,local means, Hardy - Littlewood maximal function*

**Upload:** 1999-03-01

**Update:** 2000-01-24

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