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

Triebel, Hans

Math. Nachr. 144, 189-222 (1989).

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

Keywords:

pseudo-differential operator; atomic decomposition; traces of functions; Fourier integral operator; singular integral operator

Citations:

Zbl 0551.46018

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