Vol. 68, No. 1, 1977

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On Lp, Lq multipliers of Fourier transforms

Richard Julian Bagby

Vol. 68 (1977), No. 1, 1–12
Abstract

Let m be a tempered distribution on Rn. We say m is an Lp, Lq multiplier (more briefly: m Mpq) if, for each ϕ ∈𝒮, the inverse Fourier transform of mϕ is in Lq, and there is a constant C such that ∥ℱ1(mϕ)q Cϕp for all such ϕ. The basic problem we shall consider is that of establishing sufficient conditions that a locally integrable function m Mpq in the case 1 < p < q < .

Mathematical Subject Classification
Primary: 42A18, 42A18
Milestones
Received: 12 February 1976
Published: 1 January 1977
Authors
Richard Julian Bagby