Lipschitz continuity of the dilation of Bloch functions on the unit ball of a Hilbert space and applications
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Título
Lipschitz continuity of the dilation of Bloch functions on the unit ball of a Hilbert space and applicationsAutoría
Fecha de publicación
2024-02-13Editor
SpringerISSN
2008-8752Cita bibliográfica
Miralles, A. Lipschitz continuity of the dilation of Bloch functions on the unit ball of a Hilbert space and applications. Ann. Funct. Anal. 15, 17 (2024). https://doi.org/10.1007/s43034-024-00317-0Tipo de documento
info:eu-repo/semantics/articleVersión de la editorial
https://link.springer.com/article/10.1007/s43034-024-00317-0Versión
info:eu-repo/semantics/publishedVersionPalabras clave / Materias
Resumen
Let BE be the open unit ball of a complex finite- or infinite-dimensional Hilbert space.
If f belongs to the space B(BE ) of Bloch functions on BE , we prove that the dilation
map given by x → (1 − x 2)R f (x) for ... [+]
Let BE be the open unit ball of a complex finite- or infinite-dimensional Hilbert space.
If f belongs to the space B(BE ) of Bloch functions on BE , we prove that the dilation
map given by x → (1 − x 2)R f (x) for x ∈ BE , where R f denotes the radial
derivative of f , is Lipschitz continuous with respect to the pseudohyperbolic distance
ρE in BE , which extends to the finite- and infinite-dimensional setting the result given
for the classical Bloch space B. To provide this result, we will need to prove that
ρE (zx,zy) ≤ |z|ρE (x, y) for x, y ∈ BE under some conditions on z ∈ C. Lipschitz
continuity of x → (1 − x 2)R f (x) will yield some applications on interpolating
sequences for B(BE ) which also extends classical results from B to B(BE ). Indeed,
we show that it is necessary for a sequence in BE to be separated to be interpolating for
B(BE ) and we also prove that any interpolating sequence for B(BE ) can be slightly
perturbed and it remains interpolating. [-]
Publicado en
Annals of Functional Analysis, 2024, vol. 15, no 2Entidad financiadora
Ministerio de Ciencia, Innovación y Universidades
Identificador de la entidad financiadora
http://dx.doi.org/10.13039/501100011033
Código del proyecto o subvención
MICIU/ICTI2017-2020/PID2019-106529GB-I00
Título del proyecto o subvención
Álgebras de funciones sobre grupos topológicos
Derechos de acceso
info:eu-repo/semantics/openAccess
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