JOURNAL Series A - Pure and Applied Mathematics

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66 At. Georgieva, St. Kostadinov
c○Journal of Technical University at PlovdivFundamental Sciences and Applications, Vol. 11, 2005-2006Series A-Pure and Applied MathematicsBulgaria, ISSN 1310-8271Construction of analytic functions, whichdetermine bounded Toeplitz operators onH 1 and H ∞Peyo StoilovAbstractFor f ∈ H ∞ we denote by T f the Toeplitz operator on H p , defined by∫T f h =Tf(ζ)h(ζ)1 − ζz dm(ζ), h ∈ Hp .In this paper we prove some sufficient conditions for the sequences of numbersα = (α n ) n≥0in which the functionsf ∗ αdef= ∑ ˆf(n) α n z nn≥1determine bounded Toeplitz operators T f∗α on H 1 and H ∞ for all f ∈ H ∞ .1 IntroductionLet A be the class of all functions analytic in the unit disk D = {ζ : |ζ| < 1} , m(ζ) -normalized Lebesgue measure on the circle T = {ζ : |ζ| = 1} . Let H p (0 and satisfying∫‖f‖ p H p =sup0< r< 1T|f(rζ)| p dm(ζ) < ∞, 0 Mathematics Subject Classification: Primary 30E20, 30D500 Key words and phrases: Analytic function, Toeplitz operators, Cauchy integrals, multipliers.0 Received June 15, 2005.67
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Page 68 and 69: 68 Peyo Stoilov‖f‖ H ∞ = supz
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JOURNAL Series A - Pure and Applied Mathematics

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