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Banach algebra structure in analytic tent spaces

  • Rong Yang und Xiangling Zhu EMAIL logo
Veröffentlicht/Copyright: 29. August 2025
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Abstract

In this paper, the Duhamel product is used to endow analytic tent spaces with a Banach algebra structure. The Hadamard–Bergman convolution on these spaces is also described. Additionally, the Deddens algebras of composition operators are studied.

MSC 2020: 30H99; 47B99

Funding statement: The authors are supported by the GuangDong Basic and Applied Basic Research Foundation (Grant No. 2023A1515010614).

References

[1] R. R. Coifman, Y. Meyer and E. M. Stein, Some new function spaces and their applications to harmonic analysis, J. Funct. Anal. 62 (1985), no. 2, 304–335. 10.1016/0022-1236(85)90007-2Suche in Google Scholar

[2] J. A. Deddens, Another description of nest algebras, Hilbert Space Operators, Lecture Notes in Math. 693, Springer, Berlin, (1978), 77–86. 10.1007/BFb0064662Suche in Google Scholar

[3] P. Gérard and A. Pushnitski, Unbounded Hankel operators and the flow of the cubic Szegő equation, Invent. Math. 232 (2023), no. 3, 995–1026. 10.1007/s00222-022-01176-zSuche in Google Scholar

[4] H. Guediri, M. T. Garayev and H. Sadraoui, The Bergman space as a Banach algebra, New York J. Math. 21 (2015), 339–350. Suche in Google Scholar

[5] M. T. Karaev and H. S. Mustafayev, On some properties of Deddens algebras, Rocky Mountain J. Math. 33 (2003), no. 3, 915–926. 10.1216/rmjm/1181069935Suche in Google Scholar

[6] M. T. Karaev and S. Saltan, A Banach algebra structure for the Wiener algebra W ( 𝔻 ) of the disc, Complex Var. Theory Appl. 50 (2005), no. 4, 299–305. 10.1080/02781070500032911Suche in Google Scholar

[7] B. Karapetrović and J. Mashreghi, Hadamard convolution and area integral means in Bergman spaces, Results Math. 75 (2020), no. 2, Paper No. 70. 10.1007/s00025-020-01196-2Suche in Google Scholar

[8] A. Karapetyants and S. Samko, Hadamard–Bergman convolution operators, Complex Anal. Oper. Theory 14 (2020), no. 8, Paper No. 77. 10.1007/s11785-020-01035-wSuche in Google Scholar

[9] K. Madigan and A. Matheson, Compact composition operators on the Bloch space, Trans. Amer. Math. Soc. 347 (1995), no. 7, 2679–2687. 10.1090/S0002-9947-1995-1273508-XSuche in Google Scholar

[10] J. Pau, Integration operators between Hardy spaces on the unit ball of n , J. Funct. Anal. 270 (2016), no. 1, 134–176. 10.1016/j.jfa.2015.10.009Suche in Google Scholar

[11] S. Petrovic, Deddens algebras and shift, Complex Anal. Oper. Theory 5 (2011), no. 1, 253–259. 10.1007/s11785-009-0034-0Suche in Google Scholar

[12] S. Petrovic, Spectral radius algebras, Deddens algebras, and weighted shifts, Bull. Lond. Math. Soc. 43 (2011), no. 3, 513–522. 10.1112/blms/bdq118Suche in Google Scholar

[13] S. Petrovic and D. Sievewright, Compact composition operators and Deddens algebras, Complex Anal. Oper. Theory 12 (2018), no. 8, 1889–1901. 10.1007/s11785-017-0689-xSuche in Google Scholar

[14] D. Sievewright, Deddens algebras for weighted shifts, Houston J. Math. 41 (2015), no. 3, 785–814. Suche in Google Scholar

[15] M. F. Wang and L. Zhou, Embedding derivatives and integration operators on Hardy type tent spaces, Acta Math. Sin. (Engl. Ser.) 38 (2022), no. 6, 1069–1093. 10.1007/s10114-022-0405-2Suche in Google Scholar

[16] N. M. Wigley, The Duhamel product of analytic functions, Duke Math. J. 41 (1974), 211–217. 10.1215/S0012-7094-74-04123-4Suche in Google Scholar

[17] N. M. Wigley, A Banach algebra structure for H p , Canad. Math. Bull. 18 (1975), no. 4, 597–603. 10.4153/CMB-1975-106-4Suche in Google Scholar

[18] H. Xie, J. Liu and S. Ponnusamy, Volterra-type operators on the minimal Möbius-invariant space, Canad. Math. Bull. 66 (2023), no. 2, 509–524. 10.4153/S0008439522000376Suche in Google Scholar

[19] R. Yang, L. Hu and S. Li, Generalized integration operators on analytic tent spaces, Mediterr. J. Math. 21 (2024), no. 6, Paper No. 177. 10.1007/s00009-024-02720-2Suche in Google Scholar

[20] Z. Zhang, J. Liu and S. Ponnusamy, Banach algebra structure in Besov spaces, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 119 (2025), no. 1, Paper No. 21. 10.1007/s13398-024-01689-7Suche in Google Scholar

[21] Z. Zhang, J. Liu and J. Zhou, Banach algebra structure in Q p spaces and Morrey spaces, J. Math. Anal. Appl. 545 (2025), no. 1, Paper No. 129146. 10.1016/j.jmaa.2024.129146Suche in Google Scholar

[22] K. Zhu, Operator Theory in Function Spaces, 2nd ed., Math. Surveys Monogr. 138, American Mathematical Society, Providence, 2007. 10.1090/surv/138Suche in Google Scholar

Received: 2025-04-09
Accepted: 2025-06-05
Published Online: 2025-08-29

© 2025 Walter de Gruyter GmbH, Berlin/Boston

Heruntergeladen am 6.9.2025 von https://www.degruyterbrill.com/document/doi/10.1515/gmj-2025-2069/html
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