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oai:riuma.uma.es:10630/291702026-02-03T11:10:12Zcom_10630_2254col_10630_37953

Hankel matrices acting on the Hardy space H1 and on Dirichlet spaces. Girela-Álvarez, Daniel Merchán-Álvarez, Noel Hankel, Operadores de Hilbert, Operadores en espacio de Álgebra lineal 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. When μ is the Lebesgue measure on [0,1) the operator H_μ is the classical Hilbert operator H which is bounded on H^p if 1<p< ∞, but not on H^1. J. Cima has recently proved that H is an injective bounded operator from H^1 into the space C of Cauchy transforms of measures on the unit circle. The operator H_μ is known to be well defined on H^1 if and only if μ is a Carleson measure and in such a case we have that H_μ(H^1) is contained in C. Furthermore, it is bounded from H^1 into itself if and only if μ is a 1-logarithmic 1-Carleson measure. In this paper we prove that when μ is a 1-logarithmic 1-Carleson measure then H_μ actually maps H^1 into the space of Dirichlet type D^1_0. We discuss also the range of H_μ on H^1 when μ is an α-logarithmic 1-Carleson measure (0<α<1). We study also the action of the operators H_μ on Bergman spaces and on Dirichlet spaces. 2024-01-25T08:18:47Z 2024-01-25T08:18:47Z 2024-01-25T08:18:47Z 2018-12-03 journal article Girela, D., Merchán, N. Hankel matrices acting on the Hardy space and on Dirichlet spaces. Rev Mat Complut 32, 799–822 (2019). https://doi.org/10.1007/s13163-018-0288-z https://hdl.handle.net/10630/29170 10.1007/s13163-018-0288-z eng open access Springer