Borgohain, D.; Naik, S. Weighted fractional composition operators on certain function spaces. (English) Zbl 1508.47035 Asian-Eur. J. Math. 13, No. 4, Article ID 2050082, 14 p. (2020). Summary: In this paper, we give some characterizations for the boundedness of weighted fractional composition operator \(D_{\varphi , u}^\beta\) from \(\alpha \)-Bloch spaces into weighted type spaces by deriving the bounds of its norm. Also, estimates for essential norm are obtained which gives necessary and sufficient conditions for the compactness of the operator \(D_{\varphi , u}^\beta \). MSC: 47B33 Linear composition operators 33C05 Classical hypergeometric functions, \({}_2F_1\) 26A33 Fractional derivatives and integrals 44A35 Convolution as an integral transform 30H30 Bloch spaces Keywords:Gaussian hypergeometric function; weighted-type spaces; fractional derivative; boundedness; compactness PDFBibTeX XMLCite \textit{D. Borgohain} and \textit{S. Naik}, Asian-Eur. J. Math. 13, No. 4, Article ID 2050082, 14 p. (2020; Zbl 1508.47035) Full Text: DOI References: [1] Andrews, G. E., Askey, R. and Roy, R., Special Functions (Cambridge University Press, 1999). · Zbl 0920.33001 [2] Borgohain, D. and Naik, S., Weighted fractional differentiation composition operators from mixed-norm spaces to weighted-type spaces, Int. J. Anal.2014 (2014), Article ID 301709. · Zbl 1390.30003 [3] Duren, P. L., Theory of \(H^p\) Spaces (Academic Press, New York, 1981). [4] Duren, P. L., Romberg, B. W. and Shields, A. L., Linear functionals on \(\text{H}^p\) spaces with \(0<p<1\), J. Reigne Angew. Math.238 (1969) 32-60. · Zbl 0176.43102 [5] Galindo, P., Lindstorm, M. and Stević, S., Essential norms of operators into weighted-type spaces on the unit ball, Abstr. Appl. Anal.2011 (2011), Article ID 939873. [6] Hardy, G. H. and Littlewood, J. E., Some properties of fractional integrals II, Math. Z.34 (1932) 403-439. · Zbl 0003.15601 [7] Liang, Y. X. and Zhou, Z. H., Essential norm of the product of differentiation and composition operators between Bloch-type spaces, Arch. Math.100 (2013) 347-360. · Zbl 1276.47041 [8] Madigan, K. and Matheson, A., Compact composition operators on the Bloch space, Trans. Amer. Math. Soc.347 (1995) 2679-2687. · Zbl 0826.47023 [9] Macluer, B. and Zhao, R., Essential norm of weighted composition operators between Bloch-Type spaces, Rocky Mt. J. Math.33 (2003) 1437-1458. · Zbl 1061.30023 [10] Li, S. and Stević, S., Generalized weighted composition operators from \(\alpha \)-Bloch spaces into weighted-type spaces, J. Inequal. Appl.2015 (2015). · Zbl 1338.47018 [11] Stević, S., Weighted differentiation composition operator from mixed-norm spaces to weighted type spaces, Appl. Math. Comput.211(1) (2009) 222-233. · Zbl 1165.30029 [12] Zhu, K., Bloch type spaces of analytic functions, Rocky Mountain J. Math.23(3) (1993) 1147-1177. · Zbl 0787.30019 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.