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Oscillatory kernels in certain Hardy-type spaces

Lung-Kee ChenDashan Fan — 1994

Studia Mathematica

We consider a convolution operator Tf = p.v. Ω ⁎ f with Ω ( x ) = K ( x ) e i h ( x ) , where K(x) is an (n,β) kernel near the origin and an (α,β), α ≥ n, kernel away from the origin; h(x) is a real-valued C function on n 0 . We give a criterion for such an operator to be bounded from the space H 0 p ( n ) into itself.

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