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Si studia il problema dell'esistenza di soluzioni limitate per l'equazione\(\bar \partial u = f\) sui domini pseudo-Siegel\(S = \left\{ {\zeta \in \mathbb{C}^n :\sum\limits_{j = 1}^{n - 1} {\left| {\zeta _j } \right|^{2pj} + \mathfrak{F}m\zeta _n^{p_n } - 1< 0} } \right\}\) quando il dato\(f \in C_{\left( {0,1} \right)}^\infty \left( {\bar S_p } \right)\) soddisfa alla condizione\(\zeta \left| {^k } \right|\left. f \right|< + \infty per \left| \zeta \right| \to \infty \).
Summary
We study the problem of the existence of bounded solutions for the equation\(\bar \partial u = f\) on pseudo-Siegel domains\(S = \left\{ {\zeta \in \mathbb{C}^n :\sum\limits_{j = 1}^{n - 1} {\left| {\zeta _j } \right|^{2pj} + \mathfrak{F}m\zeta _n^{p_n } - 1< 0} } \right\}\) when the data\(f \in C_{\left( {0,1} \right)}^\infty \left( {\bar S_p } \right)\) satisfies the condition\(\zeta \left| {^k } \right|\left. f \right|< + \infty per \left| \zeta \right| \to \infty \).
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Work done within the Project 40% M.U.R.S.T. «Geometria Reale e Complessa».
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Barletta, E., Parrini, C. Bounded solutions for \(\bar \partial \)-problem in pseudo-Siegel domains. Annali di Matematica pura ed applicata 168, 119–132 (1995). https://doi.org/10.1007/BF01759256
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DOI: https://doi.org/10.1007/BF01759256