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

Daniel Rider

Vol. 40 (1972), No. 3, 681–693

DOI: 10.2140/pjm.1972.40.681

Abstract

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

Mathematical Subject Classification 2000

Primary: 42A68

Secondary: 43A75

Milestones

Received: 26 October 1970

Published: 1 March 1972