Boundedness of higher order Hankel forms, factorization in potential spaces and derivations (Q2766387)

Higher order Hankel forms were introduced by \textit{S. Janson} and \textit{J. Peetre} [J. Math. Nachr. 132, 313-328 (1987; Zbl 0644.47026)] and in more algebraic form in [\textit{J. Peetre} and \textit{R. Rochberg}, Contemp. Math. 185, 283-306 (1995; Zbl 0944.47019), see also \textit{R. Rochberg}, Math. Sci. Res. Inst. Publ. 33, 155-178 (1998; Zbl 1128.47308)]. The ideas and open questions in the last paper lay the groundwork of the results in this paper. NEWLINENEWLINENEWLINEIn particular, the authors give an answer to the following question. Problem 1. Is every bounded \(n\)-th order Hankel form the sum of bounded elementary Hankel forms of lower or equal order? They also give so-called product and factorization theorems and study the problem whether every bounded derivation of \(A(\mathbb{D})\) is inner, \(\mathbb{D}\) being the unit disc. Solutions of some other related problems are also developed.