Banach envelopes of monogenic Hardy spaces (Q1038780)

Let \(\Omega \subset \mathbb{R}^m\) be an arbitrary Lipschitz domain. The author proves that the Banach envelope of Hardy type space \(\mathcal{H}^p(\Omega)\) with \(p \in (\frac{m-1}{m}, 1)\) of monogenic functions is a suitable Bergman type space of monogenic functions. This extends the classical result of \textit{P.\,L.\thinspace Duren}, \textit{B.\,W.\thinspace Romberg} and \textit{A.\,L.\thinspace Shields} [J.~Reine Angew.\ Math.\ 238, 32--60 (1969; Zbl 0176.43102)] on the unit disk in the plane. The author obtains this by developing a new approach which is of real variable nature and works for arbitrary Lipschitz domains.