Singular integral operators along surfaces of revolution

[摘要] Let h, gamma, and phi beradial functions on R-n and let Omega is an element of H-1 (Sn-1). Under certain natural conditions on gamma and phi, we obtain L-P boundedness for the singular integral operators T-alpha,T-beta f(x,x(n+1))=p.v. integral(Rn) h(\y\)Omega(y')e(i\y\-beta) \y\(-n-alpha) f(x-y, x(n+1) - gamma(\y\))dy and Tf (x,x(n+l)) = p.v. integral(Rn) h(\y\)Omega(y')\y\(-n) f(x -phi(\y\)y',x(n+1) - gamma(\y\))dy. R' We also proved the L-P boundedness for the maximal operator associated with Tf. (C) 2002 Elsevier Science (USA). All rights reserved.

[发布日期] 2002-10-15