Characterizations for certain analytic functions by series expansions with hadamard gaps

• Ahmed A. El-Sayed ^[1] ; A Kamal ^[2] ; T.I Yassen ^[3]
  1. [1] Sohag University Faculty of Science Mathematics Department
  2. [2] Port Said University Faculty of Science Department of Mathematics
  3. [3] El Azhar University at Assiut Faculty of Science Department of Mathematics

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• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 16, Nº. 1, 2014, págs. 81-94
• Idioma: inglés
• DOI: 10.4067/S0719-06462014000100008
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• Resumen
  • español

    En este artículo caracterizamos las funciones Q K,ω (p, q) por series lacunarias bajo condiciones medianas impuestas en las funciones de peso K y ω, donde Q K,ω (p, q) es un espacio de funciones analíticas definidas en el disco unitario generalizando el conocido espacio analítico del tipo Besov.

  • English

    In this paper we characterize Q K,ω (p, q) functions by lacunary series under mild conditions posed on the weight functions K and ω, where Q K,ω (p, q) is a space of analytic functions defined in the unit disk generalizing the well known analytic Besov-type space.

• Referencias bibliográficas
  • Avetisyan, K. L. (2013). Sharp inclusions and lacunary series in mixed-norm spaces on the polydisc. Complex variables and elliptic equations....
  • Baernstein II, A. (1980). Aspects of Contemporary Complex Analysis. Academic Press. London.
  • Choa, J. S. (1996). A property of series of holomorphic homogeneous polynomials with Hadamard gaps. Bull. Aust. Math. Soc. 53. 479-484
  • A. El-Sayed, Ahmed. (2009). Lacunary series in quaternion Bp,q spaces. Complex variables and elliptic equations. 54. 705-723
  • A. El-Sayed, Ahmed. (2011). Lacunary series in weighted hyperholomorphic Bp,q (G) spaces. Numerical Functional Analysis and Optimization....
  • A. El-Sayed, Ahmed. Meromorphic functions with Hadamard gaps,to appear.
  • A. El-Sayed, Ahmed,Kamal, A. Characterizations by gap series in meromorphic Qp functions, to appear.
  • A. El-Sayed, Ahmed,Kamal, A. Series expansions in some analytic function spaces, submitted.
  • Essén, M,Wulan, H,Xiao, J. (2006). Several function theoretic characterizations of Möbius invariant Q K spaces. J. Funct. Anal. 230. 78-115
  • Furdui, O. (2008). On a class of lacunary series in BMOA. J. Math. Anal. Appl. 342. 773-779
  • Garnett, J. (1981). Bounded analytic functions. Academic Press. New York.
  • Gürlebeck, K,Malonek, H. R. (2001). On strict inclusions of weighted Dirichlet spaces of monogenic functions. Bull. Aust. Math. Soc. 64. 33-50
  • Gürlebeck, K,A. El-Sayed, Ahmed. (2004). Trends in Mathematics Advances in Analysis and Geometry. Birkhäuser Verlarg Publisher. Basel.
  • Kamal, A,A. El-Sayed, Ahmed. (2013). A property of meromorphic functions with Hadamard gaps. Scientific Research and Essays. 8. 633-639
  • Mateljević, M,Pavlović, M. (1983). Lp-behavior of power series with positive coefficients and Hardy spaces. Proc. Amer. Math. Soc. 87. 309-316
  • Miao, J. (1992). A property of analytic functions with Hadamard gaps. Bull. Austral. Math. Soc. 45. 105-112
  • Rashwan, R. A,A. El-Sayed, Ahmed,Kamal, Alaa. (2009). Integral characterizations of weighted Bloch spaces and QK,ω (p, q) spaces. Mathematica....
  • Rudin, W. (1987). Real and complex analysis. MeGraw-Hill. New York.
  • Wulan, H,Zhu, K. (2007). Lacunary series in QK spaces. Studia Math. 178. 217-230
  • Wulan, H,Zhu, K. (2008). Lacunary series in QK spaces. Journal of function spaces and applications. 6. 293-301
  • Zygmund, A. (1988). Trigonometric series: Volumes I and II combined. Cambridge Mathematical Library. Cambridge University Press. Cambridge.