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oai:riuma.uma.es:10630/292792026-02-03T11:02:52Zcom_10630_2254col_10630_37953

00925njm 22002777a 4500 dc Moreno, Álvaro Miguel author Peláez-Márquez, José Ángel author De la Rosa, Elena author 2024-01-09 We establish new characterizations of the Bloch space B which include descriptions in terms of classical fractional derivatives. Being precise, for an analytic function f (z) = E∞n=0 ^f(n)zn in the unit disc D, we define the fractional derivative Dμ( f )(z) = ∞E n=0 ^f (n)/μ2n+1 zn induced by a radial weight μ, where μ2n+1 = S01r 2n+1μ(r) dr are the odd moments of μ. Then, we consider the space Bμ of analytic functions f in D such that f Bμ =supz∈D μ(z)|Dμ( f )(z)| < ∞, where μ(z) = S1 |z| μ(s) ds. We prove that Bμ is continously embedded in B for any radial weight μ, and B = Bμ if and only if μ ∈ D = D ∩ Dq. A radial weight μ ∈ D if sup0≤r<1 μ(r) μ (1+r/2) < ∞ and a radial weight μ ∈ Dq if there exist K = K(μ) > 1 such that inf0≤r<1 μ(r) μ (1− 1−r/K) > 1. Moreno, Á.M., Peláez, J.Á. & de la Rosa, E. Fractional Derivative Description of the Bloch Space. Potential Anal (2024). https://doi.org/10.1007/s11118-023-10119-z https://hdl.handle.net/10630/29279 10.1007/s11118-023-10119-z Funciones (Matemáticas) Números complejos Funciones de variable compleja Fractional derivative description of the bloch space