Sharp nonlogarithmic Kneser theorems for fourth-order elliptic equations |
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Authors: | VB Headley |
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Institution: | Department of Mathematics, Brock University, St. Catharines, Ontario, Canada |
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Abstract: | Let D(?) be the Doob's class containing all functions f(z) analytic in the unit disk Δ such that f(0) = 0 and lim on an arc A of ?Δ with length . It is first proved that if f?D(?) then the spherical norm ∥ f ∥ = supz?Δ, where C1 = limn→∞. Next, U represents the Seidel's class containing all non-constant functions f(z) bounded analytic in Δ such that almost everywhere. It is proved that inff?U∥f∥ = 0, and if f has either no singularities or only isolated singularities on ?Δ, then ∥f∥ ? C1. Finally, it is proved that if f is a function normal in Δ, namely, the norm ∥f∥< ∞, then we have the sharp estimate ∥fp∥ ? p∥f∥, for any positive integer p. |
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