RT Journal Article
T1 Fractional derivative description of the bloch space
A1 Moreno, Álvaro Miguel
A1 Peláez-Márquez, José Ángel
A1 De la Rosa, Elena
K1 Funciones (Matemáticas)
K1 Números complejos
K1 Funciones de variable compleja
AB 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 continouslyembedded 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.
PB Springer Nature
YR 2024
FD 2024-01-09
LK https://hdl.handle.net/10630/29279
UL https://hdl.handle.net/10630/29279
LA eng
NO 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
NO Funding for open access charge: Universidad Málaga/CBUA. This research was supported inpart by Ministerio de Ciencia e Innovación, Spain, project PID2022-136619NB-I00; La Junta de Andalucía,project FQM210.
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 21 ene 2026