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Register a new userCharacterizations for inner functions in certain function spaces
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For $frac12<p<infty$, $0<q<infty$ and a certain two-sided doubling weight $omega$, we characterize those inner functions $Theta$ for which $$|Theta|_{A^{p,q}_omega}^q=int_0^1 left(int_0^{2pi} |Theta(re^{itheta})|^p dthetaright)^{q/p} omega(r),dr<infty.$$ Then we show a modified version of this result for $pge q$. Moreover, two additional characterizations for inner functions whose derivative belongs to the Bergman space $A_omega^{p,p}$ are given.
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Let $mathcal{S}$ denote the family of all functions that are analytic and univalent in the unit disk $mathbb{D}:={z: |z|<1}$ and satisfy $f(0)=f^{prime}(0)-1=0$. In the present paper, we consider certain subclasses of univalent functions associated with the exponential function, and obtain the sharp upper bounds on the initial coefficients and the difference of initial successive coefficients for functions belonging to these classes.
We give conditions characterizing holomorphic and meromorphic functions in the unit disk of the complex plane in terms of certain weak forms of the maximum principle. Our work is directly inspired by recent results of John Wermer, and by the theory of the projective hull of a compact subset of complex projective space developed by Reese Harvey and Blaine Lawson.
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