A GENERALIZATION OF A RESULT OF CHOA ON ANALYTIC FUNCTIONS WITH HADAMARD GAPS

Title & Authors
A GENERALIZATION OF A RESULT OF CHOA ON ANALYTIC FUNCTIONS WITH HADAMARD GAPS
Stevic Stevo;

Abstract
In this paper we obtain a sufficient and necessary condition for an analytic function f on the unit ball B with Hadamard gaps, that is, for $f(z)\; Keywords analytic functions;Hadamard gap;Bergaman space;unit ball; Language English Cited by 1. On new Bloch-type spaces, Applied Mathematics and Computation, 2009, 215, 2, 841 2. Weighted composition operators from weighted Bergman spaces to weighted-type spaces on the unit ball, Applied Mathematics and Computation, 2009, 212, 2, 499 3. 𝒩p-type functions with Hadamard gaps in the unit ball, Complex Variables and Elliptic Equations, 2016, 61, 6, 843 4. Lacunary Series in Weighted HyperholomorphicBp,q(G) Spaces, Numerical Functional Analysis and Optimization, 2010, 32, 1, 41 5. Weighted-Hardy functions with Hadamard gaps on the unit ball, Applied Mathematics and Computation, 2009, 212, 1, 229 6. On Bloch-Type Functions with Hadamard Gaps, Abstract and Applied Analysis, 2007, 2007, 1 7. Some Sufficient Conditions for Analytic Functions to Belong to Space, Abstract and Applied Analysis, 2008, 2008, 1 8. Bloch-type functions with Hadamard gaps, Applied Mathematics and Computation, 2009, 208, 2, 416 9. A Theorem of Nehari Type on Weighted Bergman Spaces of the Unit Ball, Abstract and Applied Analysis, 2008, 2008, 1 10. Lacunary series in quaternion Bp,qspaces, Complex Variables and Elliptic Equations, 2009, 54, 7, 705 11. Integral-type operators between α-Bloch spaces and Besov spaces on the unit ball, Applied Mathematics and Computation, 2010, 216, 12, 3541 12. Sharp inclusions and lacunary series in mixed-norm spaces on the polydisc, Complex Variables and Elliptic Equations, 2013, 58, 2, 185 References 1. F. Beatrous and J. Burbea, Holomorphic Sobolev spaces on the ball, Dissertationes Math. 276 (1989), 1-57 2. G. Benke and D. C. Chang, A note on weighted Bergman spaces and the Cesaro operator, Nagoya Math. J. 159 (2000), 25-43 3. J. S. Choa, Some properties of analytic functions on the unit ball with Hadamard gaps, Complex Variables Theory Appl. 29 (1996), no. 3, 277-285 4. P. Duren, Theory of$H^p$spaces, Pure and Applied Mathematics Vol. 38, Academic Press, New York, 1970 5. J. H. Mathews, Coefficients of uniformly normal-Bloch functions, Yokohama Math. J. 21 (1973), 29-31 6. J. Miao, A property of analytic functions with Hadamard gaps, Bull. Austral. Math. Soc. 45 (1992), no. 1, 105-112 7. W. Rudin, Function theory in the unit ball of$C^n$, Grundlehren der Mathematis- chen Wissenschaften, 241, Springer-Verlag, New York-Berlin, 1980 8. J. -H. Shi, Inequalities for the integral means of holomorphic functions and their derivatives in the unit ball of$C^n$, Trans. Amer. Math. Soc. 328 (1991), no. 2, 619-637 9. A. Siskakis, Weighted integrals of analytic functions, Acta Sci. Math. 66 (2000), 651-664 10. S. Stevic, On an area inequality and weighted integrals of analytic functions, Result Math. 41 (2002), no. 3-4, 386-393 11. S. Stevic, Weighted integrals and conjugate functions in the unit disk, Acta Sci. Math. 69 (2003), no. 1-2, 109-119 12. S. Stevic, Weighted integrals of holomorphic functions on the polydisc, Z. Anal. Anwendungen 23 (2004), no. 3, 577-587 13. S. Yamashita, Gap series and$\alpha\$-Bloch functions, Yokohama Math. J. 28 (1980), no. 1-2, 31{36

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