• Corpus ID: 233231531

Note on Improved Bohr Inequality for harmonic mappings

  title={Note on Improved Bohr Inequality for harmonic mappings},
  author={Saminathan Ponnusamy and Ramakrishnan Vijayakumar},
Let D = {z ∈ C : |z| < 1} denote the open unit disk and H∞ denote the class of all bounded analytic functions f on the unit disk D with the supremum norm ‖f‖∞ := supz∈D |f(z)|. Also, let B = {f ∈ H∞ : ‖f‖∞ ≤ 1} and B0 = {ω ∈ B : ω(0) = 0}. Note that if |f(z)| = 1 for some z ∈ ∂D, then, by the maximum principle, it follows that f should be unimodular constant functions. So, one can conveniently exclude constant functions. In 1914, the following theorem was proved by Harald Bohr [4] for 0 ≤ r ≤ 1… 
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