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Lp-Lq estimates off the line of duality

Part of: Harmonic analysis in several variables Normed linear spaces and Banach spaces; Banach lattices Partial differential equations

Published online by Cambridge University Press:  09 April 2009

J.-G. Bak ,
D. McMichael  and
D. Oberlin
J.-G. Bak
Affiliation:
Department of Mathematics, Florida State Unviersity, Tallahassee, FL 32306-3027, USA, email address: back@math.fsu.edu, email address: mcmichael@math.fsu.edu, email address: oberlin@math.fsu.edu
D. McMichael
Affiliation:
Department of Mathematics, Florida State Unviersity, Tallahassee, FL 32306-3027, USA, email address: back@math.fsu.edu, email address: mcmichael@math.fsu.edu, email address: oberlin@math.fsu.edu
D. Oberlin
Affiliation:
Department of Mathematics, Florida State Unviersity, Tallahassee, FL 32306-3027, USA, email address: back@math.fsu.edu, email address: mcmichael@math.fsu.edu, email address: oberlin@math.fsu.edu
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Abstract

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Theorems 1 and 2 are known results concerning Lp–Lq 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 Lp-Lq 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.

MSC classification

Secondary: 46B70: Interpolation between normed linear spaces 42B15: Multipliers 35B45: A priori estimates

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 58 , Issue 2 , April 1995 , pp. 154 - 166
Copyright
Copyright © Australian Mathematical Society 1995

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