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Q ℒ,q ‐Scales in a Hyperbolic Setting
Author(s) -
Cerejeiras P.
Publication year - 2005
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200510283
Subject(s) - unit sphere , homogeneous , mathematics , invariant (physics) , dirac operator , hyperbolic manifold , laplace operator , mathematical analysis , pure mathematics , operator (biology) , relatively hyperbolic group , conformal map , eigenvalues and eigenvectors , hyperbolic function , mathematical physics , physics , combinatorics , quantum mechanics , biochemistry , chemistry , repressor , transcription factor , gene
Q p ‐scales arise in complex analysis as an interpolation scale between BMO, Bloch and Dirichlet spaces. They were generalized to the n‐dimensional case by means of the conformal group of the unit ball and a modified fundamental solution of the Laplacian; however, this operator is no longer invariant under the action of group in consideration. In this talk we propose an approach to Q ℒ,q ‐scales for homogeneous hyperbolic manifolds using a fundamental solution for the ( α ‐homogeneous) hyperbolic Dirac operator based on a spherical Radon transform. We present also some properties of this scales. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)