Mean Lipschitz spaces and a generalized Hilbert operator. - Merchán-Álvarez, Noel (Springer, 2018)
If μ is a positive Borel measure on the interval [0, 1) we let H_μ be the Hankel matrix H_μ={ μ_{n,k} }_{n,k} with entries μ_{n,k} =μ_{n+k} where μ_n denotes the moment of order n of μ. This matrix induces formally an operator on the space of all analytic functions in the unit disc D. This is a natural generalization of the classical Hilbert operator. In this paper we study the action of the operators H_μ on mean Lipschitz spaces of analytic functions.
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Keywords: Hankel, Operadores de; Hilbert, Operadores en espacio de; Medida, Teoría de la; Análisis matemático; Hankel matrix; Generalized Hilbert operator; Mean Lipschitz spaces; Carleson measures