振荡奇异积分的L^p有界性

L^p Boundedness for Oscillatory Singular Integrals

文中讨论了振荡奇异积分:其中对满足一定凸性条件的P以及Ω∈L^q(S^(n-1))(q>1),证明了T在L^P(R^n)上有界,p>1.

This paper considers the following oscillatory singular integrals: Tf(x)= P.V. ∫Rn eip(x-y)K(x - y)f(x)dy, where K(y) = Ω(y)/||y||n and ∫Sn-1Ω(y)dσ(y) = 0. For P which satisfies certain convex condition andΩ∈ Lq(Sn-1) (q > 1), we prove that T is bounded on Lp(Rn), p > 1.