Volterra integral operators on a family of Dirichlet-Morrey spaces

• Autorzy: Hu Lian , Liu Xiaosong

Identyfikatory

DOI

10.7494/OpMath.2023.43.5.633

• Języki publikacji: EN

Abstrakty

EN

A family of Dirichlet-Morrey spaces Dλ,K of functions analytic in the open unit disk D are defined in this paper. We completely characterize the boundedness of the Volterra integral operators Tg, Ig and the multiplication operator Mg on the space Dλ,K. In addition, the compactness and essential norm of the operators Tg and Ig on Dλ,K are also investigated.

Słowa kluczowe

EN

Dirichlet-Morrey type space; Carleson measure; Volterra integral operators; bounded operators; essential norm

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2023
• Tom: Vol. 43, no. 5
• Strony: 633--649
• Opis fizyczny: Bibliogr. 39 poz.

Twórcy

autor

Hu Lian

• Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, 610054, Chengdu, Sichuan, P.R. China

autor

Liu Xiaosong

• Department of Mathematics, JiaYing University, 514015, Meizhou, Guangdong, P.R. China

Bibliografia

• [1] A. Aleman, A. Siskakis, Integration operators on Bergman spaces, Indiana Univ. Math. J. 46 (1997), 337–356.
• [2] D.C. Chang, S. Li, S. Stević, On some integral operators on the unit polydisk and the unit ball, Taiwanese J. Math. 11 (2007), no. 5, 1251–1286.
• [3] P. Galanopoulos, N. Merchán, A. Siskakis, A family of Dirichlet–Morrey spaces, Complex Var. Elliptic Equ. 64 (2019), no. 10, 1686–1702.
• [4] P. Galindo, M. Lindström, S. Stević, Essential norm of operators into weighted-type spaces on the unit ball, Abstr. Appl. Anal. 2011 (2011), Art. ID 939873, 13 pp.
• [5] L. Hu, R. Yang, S. Li, Embedding and Volterra integral operators on a class of Dirichlet–Morrey spaces, AIMS Math. 6 (2021), no. 7, 7782–7797.
• [6] L. Hu, R. Yang, S. Li, Dirichlet–Morrey type spaces and Volterra integral operators, J. Nonlinear Var. Anal. 5 (2021), 477–491.
• [7] S. Li, S. Stević, Integral type operators from mixed-norm spaces to α-Bloch spaces, Integral Transforms Spec. Funct. 18 (2007), no. 7, 485–493.
• [8] S. Li, S. Stević, Compactness of Riemann–Stieltjes operators between F(p, q, s) spaces and α-Bloch spaces, Publ. Math. Debrecen 72 (2008), no. 1–2, 111–128.
• [9] S. Li, S. Stević, Riemann–Stieltjes operators between different weighted Bergman spaces, Bull. Belg. Math. Soc. Simon Stevin 15 (2008), no. 4, 677–686.
• [10] P. Li, J. Liu, Z. Lou, Integral operators on analytic Morrey spaces, Sci. China Math. 57 (2014), no. 9, 1961–1974.
• [11] S. Li, J. Liu, C. Yuan, Embedding theorems for Dirichlet type spaces, Canad. Math. Bull. 63 (2020), no. 1, 106–117.
• [12] J. Liu, Z. Lou, Carleson measure for analytic Morrey spaces, Nonlinear Anal. 125 (2015), 423–432.
• [13] J. Liu, Z. Lou, Properties of analytic Morrey spaces and applications, Math. Nachr. 288 (2015), 1673–1693.
• [14] J. Liu, Z. Lou, K. Zhu, Embedding of Möbius invariant function spaces into tent spaces, J. Geom. Anal. 27 (2017), no. 2, 1013–1028.
• [15] X. Liu, S. Li, R. Qian, Volterra integral operators and Carleson embedding on Campanato spaces, J. Nonlinear Var. Anal. 5 (2021), 141–153.
• [16] J. Ortega, J. Fàbrega, Pointwise multipliers and corona type decomposition in BMOA, Ann. Inst. Fourier (Grenoble) 46 (1996), no. 1, 111–137.
• [17] J. Pau, R. Zhao, Carleson measures, Riemann–Stieltjes and multiplication operators on a general family of function spaces, Integral Equations Operator Theory 78 (2014), no. 4, 483–514.
• [18] R. Qian, S. Li, Volterra type operators on Morrey type spaces, Math. Inequal. Appl. 18 (2015), no. 4, 1589–1599.
• [19] R. Qian, S. Li, Carleson measure and Volterra type operators on weighted BMOA spaces, Georgian Math. J. 27 (2020), no. 3, 413–424.
• [20] R. Qian, X. Zhu, Embedding of Qp spaces into tent spaces and Volterra integral operator, AIMS Math. 6 (2020), 698–711.
• [21] B. Sehba, S. Stević, On some product-type operators from Hardy–Orlicz and Bergman–Orlicz spaces to weighted-type spaces, Appl. Math. Comput. 233 (2014), 565–581.
• [22] C. Shen, Z. Lou, S. Li, Embedding of BMOAlog into tent spaces and Volterra integral operators, Comput. Meth. Funct. Theory 20 (2020), 1–18.
• [23] Y. Shi, S. Li, Essential norm of integral operators on Morrey type spaces, Math. Ineq. Appl. 19 (2016), no. 1, 385–393.
• [24] H.J. Schwartz, Composition operators on Hp, PhD Thesis, University of Toledo, 1969.
• [25] S. Stević, Essential norms of weighted composition operators from the α-Bloch space to a weighted-type space on the unit ball, Abstr. Appl. Anal. 2008 (2008), Article ID 279691, 11 pp.
• [26] S. Stević, On operator Pg φ from the logarithmic Bloch-type space to the mixed-norm space on unit ball, Appl. Math. Comput. 215 (2010), no. 12, 4248–4255.
• [27] S. Stević, S.I. Ueki, Integral-type operators acting between weighted-type spaces on the unit ball, Appl. Math. Comput. 215 (2009), no. 7, 2464–2471.
• [28] F. Sun, H. Wulan, Characterizations of Morrey type spaces, Canad. Math. Bull. Canad. Math. Bull. 65 (2022), no. 2, 328–344.
• [29] Z. Wu, C. Xie, Q spaces and Morrey spaces, J. Funct. Anal. 201 (2003), no. 1, 282–297.
• [30] H. Wulan, K. Zhu, Möbius Invariant QK Spaces, Springer, Cham, 2017.
• [31] H. Wulan, J. Zhou, QK and Morrey type spaces, Ann. Acad. Sci. Fenn. Math. 38 (2013), no. 1, 193–207.
• [32] J. Xiao, Holomorphic Q Classes, Lecture Notes in Mathematics, vol. 1767, Springer-Verlag, Berlin, 2001.
• [33] J. Xiao, W. Xu, Composition operators between analytic Campanato spaces, J. Geom. Anal. 24 (2014), no. 2, 649–666.
• [34] J. Xiao, C. Yuan, Analytic Campanato spaces and their compositions, Indiana Univ. Math. J. 64 (2015), no. 4, 1001–1025.
• [35] L. Yang, R. Qian, Volterra integral operator and essential norm on Dirichlet type spaces, AIMS Math. 6 (2021), no. 9, 10092–10104.
• [36] R. Yang, X. Zhu, Besov–Morrey spaces and Volterra integral operator, Math. Inequal. Appl. 24 (2021), no. 3, 857–871.
• [37] R. Zhao, On a general family of function spaces, Ann. Acad. Sci. Fenn. Math. Diss. 105 (1996), 56 pp.
• [38] J. Zhou, X. Zhu, Essential norm of a Volterra-type integral operator from Hardy spaces to some analytic function spaces, J. Integral Equations Appl. 28 (2016), no. 4, 581–593.
• [39] K. Zhu, Operator Theory in Function Spaces, 2nd ed., American Mathematical Society, Providence, 2007.

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023)