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Zbl 0944.32004
Hansson, Thomas
On Hardy spaces in complex ellipsoids. (English)
[J] Ann. Inst. Fourier 49, No.5, 1477-1501 (1999). ISSN 0373-0956; ISSN 1777-5310/e

Let $B^p$, $p=(p_1,\dots,p_n)$, $p_j\in Z^+$, be a domain with defining function $\rho(z)= \sum^n_{j=1}|z_j|^{2p_j-1}$.\par 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).\par In Theorem 5 the factorization of the function from $H^1(B^p)$ is obtained.
[P.Z.Agranovich (Khar'kov)]

MSC 2000:: *32A35 $H^p$-spaces (several complex variables)
42B20 Singular integrals, several variables

Keywords: Hardy spaces; atomic decomposition; factorization; complex ellipsoids

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