On Hardy spaces in complex ellipsoids
Let \(B^p\), \(p=(p_1,\dots,p_n)\), \(p_j\in Z^+\), be a domain with defining function \(\rho(z)= \sum^n_{j=1}|z_j|^{2p_j-1}\). Let \[ Hf (z)= \left({1\over 2\pi i}\right)^n \int_{\partial B^p}{f(\zeta) \partial \rho (\zeta)\wedge \{\bigl(\overline\partial \partial\rho (\zeta)\bigr)^{n-1} \over \bigl( \partial\rho (\zeta),\zeta- z\bigr)^n},\;z\in B^p. \] The author investigates the properties of this operator \(H\) (Theorem 1, 2, 3, 4). In Theorem 5 the factorization of the function from \(H^1(B^p)\) is obtained.
scientific article; zbMATH DE number 1355989
scientific article