Bounded solutions for 119-01119-01119-01-problem in pseudo-Siegel domains期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Bounded solutions for 119-01119-01119-01-problem in pseudo-Siegel domains

Authors:	Elisabetta Barletta Carla Parrini

Institution:	(1) Present address: Dipartimento di Matematica, Università della Basilicata, Via Nazario Sauro 85, 85100 Potenza, Italy;(2) Present address: Dipartimento di Matematica «Ulisse Dini», Università di Firenze, Viale Morgagni 67/A, 50134 Firenza, Italy

Abstract:	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 $\zeta \left\| {^k } \right\|\left. f \right\|< + \infty per \left\| \zeta \right\| \to \infty$ . Sunto 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 $\zeta \left\| {^k } \right\|\left. f \right\|< + \infty per \left\| \zeta \right\| \to \infty$ . Work done within the Project 40% M.U.R.S.T. «Geometria Reale e Complessa».

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