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Herz Classes and Toeplitz Operators in the Disk

Authors:	Maribel Loaiza Marcos López-García Salvador Pérez-Esteva

Institution:	(1) Instituto de Matemáticas, Universidad Nacional Autónoma de México, Ciudad Universitaria, 04510, D.F., México;(2) Instituto de Matemáticas, Unidad Cuernavaca, Universidad Nacional Autónoma de México, A.P. 273-3, ADMON 3, Cuernavaca, Mor., 62251, México

Abstract:	In this paper we decompose $\mathbb{D}$ into diadic annuli $\{A_n:n\in\mathbb{N}\}$ and consider the class S_p,q of Toeplitz operators T_φ for which the sequence of Schatten norms $\left( {\left\\| {T_{\varphi _n } } \right\\|_p } \right)_{n \in \mathbb{N}}$ belongs to ℓ^q, where φ_n = φχ A_n. We study the boundedness and compactness of the operators in S_p,q and we describe the operators T_φ , φ ≥ 0 in these spaces in terms of weighted Herz norms of the averaging operator of the symbols φ.

Keywords:	Primary 47B35 Secondary 46E30
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