Complex tangential characterizations of Hardy-Sobolev spaces of holomorphic functions (Q1261161)

The title describes the content of this long paper. The main result looks formally quite similar to the characterisation of Hardy-Sobolev spaces in appropriate domains of \(\mathbb{C}^ n\) in terms of the full tangential gradients \(\nabla^ k\), but it has the complex (holomorphic) tangential gradients \(\nabla_ T^{2k}\) in place of \(\nabla^ k\). This is achieved through delicate pointwise majoration of \(\nabla^ k\) by \(\nabla^ k_ T+\) ``the rest'' and is easier said than done (or described).