J Austral Math Soc Ser A 58 pp154--166, 1995.

L^p-L^q Estimates off the Line of Duality

J.-G. Bak, D. McMichael and D. Oberlin

Abstract

Theorems 1 and 2 are known results concerning L^p-L^q estimates for certain operators wherein the point (1/p, 1/q) lies on the line of duality 1/p + 1/q = 1. In Theorems 1' and 2' we show that with mild additional hypotheses it is possible to prove L^p-L^q estimates for indices (1/p, 1/q) off the line of duality. Applications to Bochner-Riesz means of negative order and uniform Sobolev inequalities are given.

1991 AMS Subject Classification: primary 46B70; secondary 42B15, 35B45

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Authors

J.-G. Bak

mailto:bak@math.fsu.edu

D. McMichael

mailto:mcmichael@math.fsu.edu

D. Oberlin

mailto:oberlin@math.fsu.edu

Department of Mathematics, Florida State University, Tallahassee, FL 32306-3027, USA.