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Let D be the unit disk centered at the origin in the complex plane. In this paper we consider an extremal problem for an area-type functional in the space B… Click to show full abstract
Let D be the unit disk centered at the origin in the complex plane. In this paper we consider an extremal problem for an area-type functional in the space B of Bloch functions with the seminorm ||b||B = sup{(1 − |z|2)|b’(z)|: z ∈ D}. We show that sup{Σk=1n k|bk|2: ||b||B ≤ 1} = nBn2, n = 1, 2, 3, 4, 5, where bk are the Taylor coefficients of b and Bn = sup{|bn|: ||b||B ≤ 1}.
Keywords:
note area;
bloch functions;
type functional;
area type
Journal Title: Lobachevskii Journal of Mathematics
Year Published: 2017
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Journal Title: Lobachevskii Journal of Mathematics
Year Published: 2017
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!