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Abstrakty
In this article, we define a convolution operator and study its boundedness on mixed-norm spaces. In particular,we obtain awell-known result on the boundedness of composition operators given by Avetisyan and Stević in [K. Avetisyan and S. Stević, The generalized Libera transform is bounded on the Besov mixednorm, BMOA and VMOA spaces on the unit disc, Appl. Math. Comput. 213 (2009), no. 2, 304-311]. Also we consider the adjoint Ab,c for b > 0 of two parameter families of Cesáro averaging operators and prove the boundedness on Besov mixed-norm spaces Bp,qα+(c−1) for c > 1.
Wydawca
Czasopismo
Rocznik
Tom
Strony
185--192
Opis fizyczny
Bibliogr. 24 poz.
Twórcy
autor
- Department of Applied Sciences, Gauhati University, Guwahati 781014, India
autor
- Department of Applied Sciences, Gauhati University, Guwahati 781014, India
Bibliografia
- [1] M. R. Agrawal, P. G. Howlett, S. K. Lucas, S. Naik and S. Ponnusamy, Boundedness of generalized Cesáro averaging operators on certain function spaces, J. Comput. Appl. Math. 180 (2005), no. 2, 333-344.
- [2] A. Aleman and J. A. Cima, An integral operator on Hp and Hardy’s inequality, J. Anal. Math. 85 (2001), 157-176.
- [3] G. E. Andrews, R. Askey and R. Roy, Special Functions, Encyclopedia Math. Appl. 71, Cambridge University, Cambridge, 1999.
- [4] K. Avetisyan and S. Stević, The generalized Libera transform is bounded on the Besov mixed-norm, BMOA and VMOA spaces on the unit disc, Appl. Math. Comput. 213 (2009), no. 2, 304-311.
- [5] D. Borgohain and S. Naik, Generalized Cesàro operators on the spaces of Cauchy transforms, Acta Sci. Math. (Szeged) 83 (2017), no. 1-2, 143-154.
- [6] P. L. Duren, Theory of Hp Spaces, Pure Appl. Math. 38, Academic Press, New York, 1970.
- [7] H. Hedenmalm, B. Korenblum and K. Zhu, Theory of Bergman Spaces, Grad. Texts in Math. 199, Springer, New York, 2000.
- [8] Z. Hu, Extended Cesàro operators on Bergman spaces, J. Math. Anal. Appl. 296 (2004), no. 2, 435-454.
- [9] O. S. Kwon and N. E. Cho, A class of nonlinear integral operators preserving double subordinations, Abstr. Appl. Anal. 2008 (2008), Article ID 792160.
- [10] S. Li and S. Stević, Integral type operators from mixed-norm spaces to α-Bloch spaces, Integral Transforms Spec. Funct. 18 (2007), no. 7-8, 485-493.
- [11] S. Li and S. Stević, Generalized composition operators on Zygmund spaces and Bloch type spaces, J. Math. Anal. Appl. 338 (2008), no. 2, 1282-1295.
- [12] S. Li and S. Stević, Products of composition and integral type operators from H∞ to the Bloch space, Complex Var. Elliptic Equ. 53 (2008), no. 5, 463-474.
- [13] S. Li and S. Stević, Products of Volterra type operator and composition operator from H∞ and Bloch spaces to Zygmund spaces, J. Math. Anal. Appl. 345 (2008), no. 1, 40-52.
- [14] S. Li and S. Stević, Riemann-Stieltjes operators between different weighted Bergman spaces, Bull. Belg. Math. Soc. Simon Stevin 15 (2008), no. 4, 677-686.
- [15] S. Li and S. Stević, Riemann-Stieltjes operators between mixed norm spaces, Indian J. Math. 50 (2008), no. 1, 177-188.
- [16] S. Li and S. Stević, Products of integral-type operators and composition operators between Bloch-type spaces, J. Math. Anal. Appl. 349 (2009), no. 2, 596-610.
- [17] S. Naik, Generalized Cesáro operators on mixed norm spaces, J. Indian Acad. Math. 31 (2009), no. 1, 295-306.
- [18] S. Naik, Generalized Cesàro operators on certain function spaces, Ann. Polon. Math. 98 (2010), no. 2, 189-199.
- [19] S. Naik, Cesáro type operators on spaces of analytic functions, Filomat 25 (2011), no. 4, 85-97.
- [20] A. G. Siskakis, Semigroups of composition operators in Bergman spaces, Bull. Austral. Math. Soc. 35 (1987), no. 3, 397-406.
- [21] K. Stempak, Cesàro averaging operators, Proc. Roy. Soc. Edinburgh Sect. A 124 (1994), no. 1, 121-126.
- [22] S. Stević, Cesàro averaging operators, Math. Nachr. 248/249 (2003), 185-189.
- [23] N. M. Temme, Special Functions, John Wiley & Sons, New York, 1996.
- [24] J. Xiao, Cesàro-type operators on Hardy, BMOA and Bloch spaces, Arch. Math. (Basel) 68 (1997), no. 5, 398-406.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).
Typ dokumentu
Bibliografia
Identyfikator YADDA
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