A rough hypersingular integral operator with an oscillating factor

作者：Chen Daning; Fan Dashan; Le Hung Viet^*

来源：Journal of Mathematical Analysis and Applications, 2006, 322(2): 873-885.

DOI：10.1016/j.jmaa.2005.09.070

• singular integrals
• Hardy spaces on spheres
• maximal operators
• Sobolev spaces

We study certain hypersingular integrals F(Omega,alpha,beta) f defined on all test functions f is an element of P(R(n)), where the kernel of the operator F(Omega,alpha,beta) has a strong singularity vertical bar y vertical bar(-n-alpha) (alpha > 0) at the origin, an oscillating factor e(i vertical bar y vertical bar-beta) (beta > 0) and a distribution Omega is an element of H(r)(S(n-1)), 0 < r < 1. We show that F(Omega,alpha,beta) extends to a bounded linear operator from the Sobolev space L(gamma)(P) boolean AND L(P) to the Lebesgue space L(P) for beta/(beta - alpha) < p < beta/alpha, if y the distribution Q is in the Hardy space H(r)(S(n-1)) with 0 < r = (n - 1)/(n - 1 + gamma) (0 < y <= alpha) and beta > 2 alpha > 0.

• 出版日期2006-10-15
• 单位华中师范大学