Oscillatory kernels in certain Hardy-type spaces

ArticleOriginal scientific text

Title

Authors ¹, ²

Department of Mathematics, Oregon State University, Corvallis, Oregon 97331, U.S.A.
Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201, U.S.A.

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^{\infty}

function on

ℝ^{n} ∖ {0}

. We give a criterion for such an operator to be bounded from the space

H^{p}_{0} (ℝ^{n})

into itself.

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