Oscillatory kernels in certain Hardy-type spaces
Tom 111 / 1994
Studia Mathematica 111 (1994), 195-206
DOI: 10.4064/sm-111-2-195-206
Streszczenie
We consider a convolution operator Tf = p.v. Ω ⁎ f with $Ω(x) = K(x)e^{ih(x)}$, 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 $ℝ^n ∖ {0}$. We give a criterion for such an operator to be bounded from the space $H^{p}_{0}(ℝ^n)$ into itself.
