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A family of Dirichlet Morrey spaces.
Galanopoulos, Petros; Merchán-Álvarez, Noel; Siskakis, Aristomenis G. (Taylor & Francis, 2019-02-03)To each weighted Dirichlet space D_p, 0<p<1, we associate a family of Morrey-type spaces D_{λ,p}, 0<λ<1, constructed by imposing growth conditions on the norm of hyperbolic translates of functions. We indicate some of the ... -
Cesàro-like operators acting on spaces of analytic functions
Galanopoulos, Petros; Girela-Álvarez, Daniel; Merchán-Álvarez, Noel (Springer, 2022-03-17)Let D be the unit disc in C. If μ is a finite positive Borel measure on the interval [0, 1) and f is an analytic function in D, f(z)=∑∞n=0anzn (z∈D), we define Cμ(f)(z)=∑n=0∞μn(∑k=0nak)zn,z∈D, where, for n≥0, μn denotes ... -
Cesàro-type operators associated with Borel measures on the unit disc acting on some Hilbert spaces of analytic functions
Galanopoulos, Petros; Girela-Álvarez, Daniel; Merchán-Álvarez, Noel (Elsevier, 2023)Given a complex Borel measure μon the unit disc D={z∈C:|z| <1}, we consider the Cesàro-type operator Cμdefined on the space Hol(D)of all analytic functions in Das follows: If f∈Hol(D), f(z) = ∞n=0anzn(z∈D), then Cμ(f)(z) ... -
Operators induced by radial measures acting on the Dirichlet space
Galanopoulos, Petros; Girela-Álvarez, Daniel; Mas, Alejandro; Merchán, Noel (Springer, 2023)Let D be the unit disc in the complex plane. Given a positive finite Borel measure μ on the radius [0, 1), we let μn denote the n-th moment of μ and we deal with the action on spaces of analytic functions in D of the ...