Abstract
We consider singular integral operators of the form (a)Z1L−1Z2, (b)Z1Z2L−1, and (c)L−1Z1Z2, where Z1 and Z2 are nonzero right-invariant vector fields, and L is the L2-closure of a canonical Laplacian. The operators (a) are shown to be bounded on Lp for all p∈(1, ∞) and of weak type (1, 1), whereas all of the operators in (b) and (c) are not of weak type (p, p) for any p∈[1, ∞).
Funding Statement
Research supported by the Australian Research Council.
Note
Research carried out as a National Research Fellow.
Citation
G. I. Gaudry. T. Qian. P. Sjögren. "Singular integrals associated to the Laplacian on the affine group ax+b." Ark. Mat. 30 (1-2) 259 - 281, 1992. https://doi.org/10.1007/BF02384874
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