Singular integrals associated to the Laplacian on the affine groupax+b |
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| Authors: | G I Gaudry T Qian and P Sj?gren |
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| Institution: | (1) School of Information Science and Technology, The Flinders University of South Austrlia, PO Box 2100, 5001 Adelaide, S.A., Australia;(2) Department of Mathematics, University of New England, 2350 Armidale, NSW, Australia;(3) Department of Mathematics, Chalmers University of Technology, S-412 96 G?teborg, Sweden;(4) University of G?teborg, S-412 96 G?teborg, Sweden |
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| Abstract: | We consider singular integral operators of the form (a)Z
1L−1Z2, (b)Z
1Z2L−1, and (c)L
−1Z1Z2, whereZ
1 andZ
2 are nonzero right-invariant vector fields, andL is theL
2-closure of a canonical Laplacian. The operators (a) are shown to be bounded onL
p for allp∈(1, ∞) and of weak type (1, 1), whereas all of the operators in (b) and (c) are not of weak type (p, p) for anyp∈1, ∞).
Research supported by the Australian Research Council.
Research carried out as a National Research Fellow. |
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| Keywords: | |
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