Homogeneous Besov Research Articles

Maximal subspaces of Besov spaces invariant under multiplication by characters

Unlike the familiar L p {L^p} spaces, neither the homogeneous Besov spaces nor the H p {H^p} spaces, 0 > p > 1 0\, > \,p\, > \,\,1 , are closed under multiplication by the functions x → e i ⟨ x , h ⟩ x\, \to \,{e^{i\left \langle {x,h} \right \rangle }} . We determine the maximal subspace of these spaces which are closed under multiplication by these functions, which are the characters of R n {R^n} .