Local means and atoms in vector-valued function spaces

Details Local means and atoms in vector-valued function spaces Local means and atoms in vector-valued function spaces

2011-03-31

arxiv.org/abs/1103.6159v1

Benjamin Scharf. Local means and atoms in vector-valued function spaces. Jenaer Schriften zur Mathematik und Informatik, (Math

Mathematics

Functional Analysis

46 pages

Scientific paper

The first part of this paper deals with the topic of finding equivalent norms and characterizations for vector-valued Besov and Triebel-Lizorkin spaces. We will deduce general criteria by transferring and extending a theorem of Bui, Paluszynski and Taibleson from the scalar to the vector-valued case. By using special norms and characterizations we will derive necessary and sufficient conditions for belonging to a vector-valued function spaces. It will be shown that an element of the Schwartz space belongs to a function space if and only if it can be written as a linear combination of harmonic atoms resp. quarks with suitable conditions for the coefficients.

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