## Atomic decompositions of $$F^ s_{pq}$$ spaces. Applications to exotic pseudodifferential and Fourier integral operators.(English)Zbl 0766.46020

The author describes an atomic decomposition for the spaces $$F^ s_{pq}$$ $$(-\infty<s<\infty,\;0<p\leq 1<q\leq\infty)$$. Some times earlier, another atomic decomposition for these spaces was obtained by M. Frazier and B. Jawerth [Indiana Univ. Math. J. 34, 777-799 (1985; Zbl 0551.46018)] which was based on the same atoms. The decomposition is applied to several topics: traces of functions from $$F^ s_{pq}(\mathbb{R}^ n)$$ on $$\mathbb{R}^{n-1}$$, action of some operators (pseudo-differential, Fourier integral, singular integral) on $$F^ s_{pq}$$. Precise formulations are quite lengthy.
Reviewer: N.M.Zobin (Haifa)

### MSC:

 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 47G30 Pseudodifferential operators 47G10 Integral operators

Zbl 0551.46018
Full Text:

### References:

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