Group invariance and L p -bounded operators
Identifieur interne : 000998 ( Main/Exploration ); précédent : 000997; suivant : 000999Group invariance and L p -bounded operators
Auteurs : Toshiyuki Kobayashi [Japon] ; Andreas Nilsson [Suède]Source :
- Mathematische Zeitschrift [ 0025-5874 ] ; 2008-10-01.
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Abstract
Abstract: The Hilbert and Riesz transforms can be characterized up to scalar as the translation invariant operators that satisfy additionally certain relative invariance of conformal transformation groups. In this article, we initiate a systematic study of translation invariant operators from group theoretic viewpoints, and formalize a geometric condition that characterizes specific multiplier operators uniquely up to scalar by means of relative invariance of affine subgroups. After providing some interesting examples of multiplier operators having “large symmetry”, we classify which of these examples can be extended to continuous operators on L p (R n ) (1 < p < ∞).
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DOI: 10.1007/s00209-007-0277-2
Affiliations:
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