Journal of the Australian Mathematical Society

Research Article

ESTIMATES FOR SINGULAR INTEGRALS ALONG SURFACES OF REVOLUTION

SHUICHI SATOa1

a1 Department of Mathematics, Faculty of Education, Kanazawa University, Kanazawa 920-1192, Japan (email: shuichi@kenroku.kanazawa-u.ac.jp)

Abstract

We prove certain Lp estimates (1<p<) for nonisotropic singular integrals along surfaces of revolution. The singular integrals are defined by rough kernels. As an application we obtain Lp boundedness of the singular integrals under a sharp size condition on their kernels. We also prove a certain estimate for a trigonometric integral, which is useful in studying nonisotropic singular integrals.

(Received November 27 2006)

(Accepted May 08 2008)

2000 Mathematics subject classification

  • primary 42B20;
  • 42B25

Keywords and phrases

  • nonisotropic singular integrals;
  • extrapolation;
  • trigonometric integrals