Vol. 233, No. 2, 2007
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Strongly singular integrals along curves

Norberto Laghi & Neil Lyall

Abstract

We obtain L2 bounds for strongly singular integral operators along curves in Rd. Our results both generalize and extend to higher dimensions the planar results of Chandarana. In addition, we show that these operators are bounded from Llog L to weak L1 at the critical exponent α = 0.
Keywords

strongly singular integrals, Radon transforms

Mathematical Subject Classification

Primary: 44A12, 42B20
Authors
Norberto Laghi
School of Mathematics and Maxwell Institute for Mathematical Sciences
JCM Building, The King's Buildings
The University of Edinburgh
Edinburgh EH9 3JZ
United Kingdom
Neil Lyall
Department of Mathematics
Boyd Graduate Studies Research Center
The University of Georgia
Athens, GA 30602
United States