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Details of Grant 

EPSRC Reference: GR/J65594/01
Title: SINGULAR INTEGRALS WITH NON-STANDARD HOMOGENEITIES
Principal Investigator: Carbery, Professor A
Other Investigators:
Researcher Co-Investigators:
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Department: Sch of Mathematical & Physical Sciences
Organisation: University of Sussex
Scheme: Standard Research (Pre-FEC)
Starts: 01 October 1994 Ends: 01 January 1995 Value (£): 104,849
EPSRC Research Topic Classifications:
Mathematical Analysis
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Summary on Grant Application Form
We propose to investigate the basic real variable structure of singular integrals and associated maximal functions whose homogeneity structure is incompatible with the homogeneity of the underlying space. Let G be a homogeneous nilpotent Lie group together with a family of dilations which are not necessarily automorphisms. Let S be an averaging operator on G. We shall examine the maximal operator Mf singular integral operator Tf generated by the action of the dilations on S. We shall investigate the boundedness properties of M and T on the Lebesgue spaces defined on G. We shall also be concerned with various simpler models derived as a consequence of de Leeuw's theorem.
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Organisation Website: http://www.sussex.ac.uk