Duality of hardy space with bmo on the shilov boundary of the product domain in C2

Ji Li

Duality of hardy space with bmo on the shilov boundary of the product domain in C²

^*Corresponding author for this work

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Abstract

In this paper, we introduce the BMO space via heat kernels on M̃, where M̃ = M₁ × · · ·× M_n is the Shilov boundary of the product domain in C²ⁿ defined by Nagel and Stein ([16], see also [17]), each M_i is the boundary of a weakly pseudoconvex domain of finite type in C² and the vector fields of Mi are uniformly of finite type ([14]). And we prove that it is the dual space of product Hardy space H¹(M̃) introduced in [11].

Original language	English
Pages (from-to)	81-105
Number of pages	25
Journal	Taiwanese Journal of Mathematics
Volume	14
Issue number	1
Publication status	Published - Feb 2010
Externally published	Yes

Cite this

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abstract = "In this paper, we introduce the BMO space via heat kernels on {\~M}, where {\~M} = M1 × · · ·× Mn is the Shilov boundary of the product domain in C2n defined by Nagel and Stein ([16], see also [17]), each Mi is the boundary of a weakly pseudoconvex domain of finite type in C2 and the vector fields of Mi are uniformly of finite type ([14]). And we prove that it is the dual space of product Hardy space H1({\~M}) introduced in [11].",

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AB - In this paper, we introduce the BMO space via heat kernels on M̃, where M̃ = M1 × · · ·× Mn is the Shilov boundary of the product domain in C2n defined by Nagel and Stein ([16], see also [17]), each Mi is the boundary of a weakly pseudoconvex domain of finite type in C2 and the vector fields of Mi are uniformly of finite type ([14]). And we prove that it is the dual space of product Hardy space H1(M̃) introduced in [11].

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Duality of hardy space with bmo on the shilov boundary of the product domain in C²

Abstract

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