It is proved that the Hörmander B loc p,k (Ω 1 × Ω 2 ) and B locA similar result for weighted L p -spaces of entire analytic functions is also obtained. Finally a result on iterated Besov spaces is given: B s 2,q (R n , B s 2,q (R m )) and B s 2,q (R n+m ) are not isomorphic when 1 < q = 2 < ∞.

The weighted L p -spaces of entire analytic functions are generalized to the vector-valued setting. In particular, it is shown that the dual of the spaceThis result allows us to give some new characterizations of the so-called UMD-property and to represent several ultradistribution spaces by means of spaces of vector sequences.

In this paper we introduce the variable exponent Hörmander spaces and we study some of their properties. In particular, it is shown that B c p(•) (Ω) is isomorphic to B loc p (•) (Ω) (Ω open set in R n , p − > 1 and the Hardy-Littlewood maximal operator M is bounded in L p(•)) extending a Hörmander's result to our context. As a consequence, a number of results on sequence space representations of variable exponent Hörmander spaces are given.

No abstract

It is shown that B lock Beurling-Björck weight) extending a Hörmander's result (the proof we give is valid in the vector-valued case, too). As a consequence, and using Vogt's representation theorems and weighted L p -spaces of entire analytic functions, a number of results on sequence space representations of Hörmander-Beurling are given.