Actions
  • shareshare
  • link
  • cite
  • add
add
auto_awesome_motion View all 5 versions
Publication . Article . Preprint . 2021

Integration Operators in Average Radial Integrability Spaces of Analytic Functions

Tanausú Aguilar-Hernández; Manuel D. Contreras; Luis Rodríguez-Piazza;
Open Access
Published: 01 Jan 2021 Journal: Mediterranean Journal of Mathematics, volume 18 (issn: 1660-5446, eissn: 1660-5454, Copyright policy )
Publisher: Springer Science and Business Media LLC
Country: Spain
Abstract

In this paper we characterize the boundedness, compactness, and weak compactness of the integration operators Tg(f)(z) = ˆ z 0 f(w)g (w) dw acting on the average radial integrability spaces RM(p, q). For these purposes, we develop different tools such as a description of the bidual of RM(p, 0) and estimates of the norm of these spaces using the derivative of the functions, a family of results that we call Littlewood–Paley type inequalities. Ministerio de Economía y Competitividad, Spain, and the European Union (FEDER) PGC2018-094215-13-100 Junta de Andalucía, Spain FQM133 Junta de Andalucía, Spain FQM-104

Subjects by Vocabulary

Microsoft Academic Graph classification: Pure mathematics Mathematics Type (model theory) Compact space Analytic function Derivative

Subjects

General Mathematics, Mixed norm spaces, Integration operator, Littlewood–Paley type inequalities, Mathematics - Functional Analysis, 30H20 (Primary), 47B33 (Primary), 47D06 (Primary), 46E15(Secondary), 47G10(Secondary), Functional Analysis (math.FA), FOS: Mathematics

Related Organizations
27 references, page 1 of 3

[1] T. Aguilar-Hernández, M.D. Contreras, and L. Rodríguez-Piazza, Average radial integrability spaces of analytic functions. Preprint. ArXiv:2002.12264.

[2] A. Aleman and A.G. Siskakis, An integral operator on Hp, Complex Variables Theory Appl. 28 (1995), 149-158.

[3] A. Aleman and A.G. Siskakis, Integration operators on Bergman spaces, Indiana Univ. Math. J. 46 (1997), 337-356. [OpenAIRE]

[4] I. Arévalo, M.D. Contreras, and L. Rodríguez-Piazza, Semigroups of composition operators and integral operators on mixed norm spaces, Revista Matemática Complutense 32 (2019), 767-798.

[5] M. Basallote, M.D. Contreras, C. Hernández-Mancera, M. J. Martín, and P. J. Paúl, Volterra operators and semigroups in weighted Banach spaces of analytic functions, Collect. Math. 65 (2014), 233-249. [OpenAIRE]

[6] C. Bessaga and A. Pełczyński, On bases and unconditional convergence of series in Banach spaces, Studia Math., 17 (1958), 151-168.

[7] O. Blasco, M.D. Contreras, S. Díaz-Madrigal, J. Martínez, M. Papadimitrakis, and A. G. Siskakis, Semigroups of composition operators and integral operators in spaces of analytic functions, Ann. Acad. Sci. Fenn. Math. 38 (2013), 67-89.

[8] M.D. Contreras, J.A. Peláez, Ch. Pommerenke, and J. Rättyä, Integral operators mapping into the space of bounded analytic functions, Journal of Functional Analysis 271 (2016), 2899-2943.

[9] J.B. Conway, A Course in Functional Analysis, Graduate texts in mathematics, Springer 96, New York, 1990.

[10] J. Diestel, Sequences and Series in Banach Spaces, Graduate Text in Math., Springer, 92, New York, 1984.

moresidebar