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The standard Radon transform of holomorphic functions is not always welldefined, as the integration of such functions over planes may not converge. Inthis paper, we introduce new Radon-type transforms of co-(real)dimension $2$for harmonic and holomorphic functions on the unit ball. These transforms areabstractly defined as orthogonal projections onto spaces of complex harmonicand holomorphic plane waves, respectively. The inversion formulas are derivedbased on the dual transform, while the latter is defined as an integration on acomplex Stiefel manifold. Our transforms are extended to the Fock space andgive rise to a new transform defined on the entire $L^{2}(\mathbb{R}^{n})$through the Segal-Bargmann transform. Furthermore, we develop these transformsfor Hermitian monogenic functions on the unit ball, thereby refining theSzeg\"o-Radon transform for monogenic functions introduced by Colombo, Sabadiniand Sommen.

Radon-type transforms for holomorphic and Hermitian monogenic functions