Tytuł artykułu
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Abstrakty
In this article, we use a particular case of convolution as an operator to discuss a number of problems concerning multiplier results between function spaces such as Hardy and Bp-spaces. As a consequence, we extend certain well-known results on fractional derivatives and fractional integrals. Also, we find condition on the parameters b, c such that Pb,c in Bp.
Wydawca
Czasopismo
Rocznik
Tom
Strony
91--98
Opis fizyczny
Bibliogr. 20 poz.
Twórcy
autor
- Department of Applied Sciences, Gauhati University, Guwahati, 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] G. D. Anderson, M. K. Vamanamurthy and M. K. Vuorinen, Conformal Invariants, Inequalities, and Quasiconformal Maps, John Wiley & Sons, New York, 1997.
- [3] G. E. Andrews, R. Askey and R. Roy, Special Functions, Encyclopedia Math. Appl. 71, Cambridge University, Cambridge, 1999.
- [4] R. Balasubramanian and S. Ponnusamy, On Ramanujan asymptotic expansions and inequalities for hypergeometric functions, Proc. Indian Acad. Sci. Math. Sci. 108 (1998), no. 2, 95-108.
- [5] R. Balasubramanian, S. Ponnusamy and M. Vuorinen, On hypergeometric functions and function spaces, J. Comput. Appl. Math. 139 (2002), no. 2, 299-322.
- [6] D. Borgohain and S. Naik, An integral type operator on analytic function spaces, J. Anal. 27 (2019), no. 3, 829-836.
- [7] P. L. Duren, On the multipliers of Hp spaces, Proc. Amer. Math. Soc. 22 (1969), 24-27.
- [8] P. L. Duren, Theory of Hp Spaces, Academic Press, New York, 2000.
- [9] P. L. Duren, B. W. Romberg and A. L. Shields, Linear functionals on Hp spaces with 0< p< 1, J. Reine Angew. Math. 238 (1969), 32-60.
- [10] P. L. Duren and A. L. Shields, Properties of Hp (0< p< 1) and its continuing Banach space, Trans. Amer. Math. Soc. 141 (1969), 255-262.
- [11] P. L. Duren and A. L. Shields, Coefficient multipliers of Hp and Bp spaces, Pacific J. Math. 32 (1970), 69-78.
- [12] G. H. Hardy and J. E. Littlewood, Some properties of fractional integrals. II, Math. Z. 34 (1932), no. 1, 403-439.
- [13] I. R. Kayumov, D. M. Khammatova and S. Ponnusamy, On the Bohr inequality for the Cesáro operator, C. R. Math. Acad. Sci. Paris 358 (2020), no. 5, 615-620.
- [14] J. E. Littlewood and R. E. A. C. Paley, Theorems on Fourier series and power series (II), Proc. Lond. Math. Soc. (2) 42 (1936), no. 1, 52-89.
- [15] G. Liu and S. Ponnusamy, On harmonic ν-Bloch and ν-Bloch-type mappings, Results Math. 73 (2018), no. 3, Paper No. 90.
- [16] S. Naik, Cesáro type operators on spaces of analytic functions, Filomat 25 (2011), no. 4, 85-97.
- [17] S. Ponnusamy and F. Rø nning, Duality for Hadamard products applied to certain integral transforms, Complex Variables Theory Appl. 32 (1997), no. 3, 263-287.
- [18] S. Ponnusamy and F. Rø nning, Integral transforms of functions with the derivative in a halfplane, Israel J. Math. 114 (1999), 177-188.
- [19] K. Stempak, Cesàro averaging operators, Proc. Roy. Soc. Edinburgh Sect. A 124 (1994), no. 1, 121-126.
- [20] 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 SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-a8136922-c9f3-42ae-ac4b-0d23b86029a3