RT Journal Article
T1 Inequalities on tent spaces and closed range integration operators on spaces of average radial integrability
A1 Aguilar-Hernández, Tanausú
A1 Galanopoulos, Petros
K1 Integrales
K1 Coordenadas curvilíneas
K1 Matemáticas aplicadas
AB We deal with a reverse Carleson measure inequality for the tent spaces of analytic functions inthe unit disc D of the complex plane. The tent spaces of measurable functions were introducedby Coifman, Meyer and Stein. Let 1 ≤ p, q < ∞ and consider the measurable set G ⊆ D.We prove a necessary and sufficient condition on G in order to exist a constant K > 0 suchthatTβ (ξ )∩G| f (z)|p dm(z)1 − |z| q/p|dξ | ≥ KT1/2(ξ )| f (z)|p dm(z)1 − |z| q/p|dξ |,for any analytic function f in D with the property, the right term of the inequality above isfinite. Here T stands for the unit circle, dm(z) is the area Lebesgue measure in D and β(ξ )is the cone-like regionβ(ξ ) = {z ∈ D |z| < β} ∪  |z|<β[z, ξ ), β ∈ (0, 1),with vertex at ξ ∈ T. This work extends the study of D. Luecking on Bergman spaces to theanalytic tent spaces. We apply this result in order to characterize the closed range propertyof the integration operatorTg( f )(z) = z0f (w)g	(w) dw, z ∈ D,when acting on the average radial integrability spaces. The Hardy and the Bergman spacesform part of this family. The function g is a fixed analytic function in the unit disc. Theoperator Tg is known as Pommerenke operator. Moreover, for the first time, we provideexamples of symbols g that introduce or not a closed range operator Tg in these spaces.
PB Springer Nature
SN 1578-7303
YR 2025
FD 2025-06-12
LK https://hdl.handle.net/10630/38698
UL https://hdl.handle.net/10630/38698
LA eng
NO Aguilar-Hernández, T., Galanopoulos, P. Inequalities on tent spaces and closed range integration operators on spaces of average radial integrability. Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 119, 70 (2025).
NO Funding for open access charge: Universidad de Málaga / CBUA
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 3 mar 2026