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Unboundedness of the Ball Bilinear Multiplier Operator

Published online by Cambridge University Press:  11 January 2016

Geoff Diestel  and
Loukas Grafakos
Geoff Diestel
Affiliation:
Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA diestelg@math.sc.edu
Loukas Grafakos
Affiliation:
Department of Mathematics, University of Missouri, Columbia, MO 65211, USA, loukas@math.missouri.edu
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Abstract

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For all n > 1, the characteristic function of the unit ball in ℝ2n is not the symbol of a bounded bilinear multiplier operator from Lp (ℝn ) × Lq (ℝn ) to Lr (ℝn ) when 1/p + 1/q = 1/r and exactly one of p, q, or r′ = r/(r – 1) is less than 2.

Keywords

43B2042B2546B7047B38

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 185 , 2007 , pp. 151 - 159
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2007

References

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