Local means and atoms in vector-valued function spaces
نویسنده
چکیده
The first part of this paper deals with the topic of finding equivalent norms and characterizations for vector-valued Besov and Triebel-Lizorkin spaces Bs p,q(E) and F s p,q(E). We will deduce general criteria by transferring and extending a theorem of Bui, Paluszyński 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 Bs p,q(E) or F s p,q(E). It will be shown that an element of S ′(Rn, E) 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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