H^p-estimates of holomorphic division formulas

Pointwise multipliers and corona type decomposition in $BMOA$

“…Results of this type for Hardy spaces, have been studied by many authors, among them L. Carleson [C], E. Amar [A], M. Andersson and H. Carlsson [AnCal], [AnCa2], S.Y. Li [Li] and K.C.…”

Estimates of solutions of the $H^p$ and BMOA corona problem

“…However, in the strictly pseudoconvex case the H p -corona theorem is true for any p < ∞. This was proved by Amar, [1], (for two generators) in the ball, and in general strictly pseudoconvex domains in [9] and [10]. However, in these papers there is no good control of the dependence of δ.…”

“…However, in these papers there is no good control of the dependence of δ. The proofs in [1] and [9] use the Koszul complex, whereas the proof in [10] uses explicit holomorphic division formulas. However, in all three papers some analog of Wolff's approach to the corona problem is involved, and the starting point is the trivial pointwise minimal solution ψ =ḡ/|g| 2 to the division problem.…”

DIVISION PROBLEM IN GENERALIZED GROWTH SPACES ON THE UNIT BALL IN ℂn

“…Formulas for explicit solutions of such division problems were studied by many authors in various situations and norms (see [1], [2], [3], [4], [5], [11], [12], [14], [15], [16], [17], [18]). In particular, the H p -corona problem asks for the condition on holomorphic n-tuples G = ( …”