Abstract
Convolution operators T f ( x ) = ∫ f ( x y − 1 ) K ( y ) d y Tf(x) = \smallint f(x{y^{ - 1}})K(y)\;dy on a class of nilpotent Lie groups are shown to be bounded on L p , 1 > p > ∞ {L^p},\;1 > p > \infty , provided the Euclidean Fourier transform of K K (with respect to a coordinate system in which the group multiplication is in a special form) satisfies familiar “multiplier” conditions.
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