Vol. 40, No. 3, 1972

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Functions which operate on Lp(T), 1 < p < 2

Daniel Rider

Vol. 40 (1972), No. 3, 681–693
Abstract

Lp(T) is the algebra of Fourier transforms of functions in Lp of the circle. It is shown that if F is defined on the plane and the composition F ϕ ∈ℱL1 whenever ϕ ∈ℱLp then for all 𝜖 > 0,F(z) = P(z,z) + O(|z|q∕2𝜖) where P is a polynomial in z and z and p1 + q1 = 1(1 < p < 2).

Mathematical Subject Classification 2000
Primary: 42A68
Secondary: 43A75
Milestones
Received: 26 October 1970
Published: 1 March 1972
Authors
Daniel Rider