Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Singular integrals in product domains and the method of rotations

Author: Donald Krug
Journal: Proc. Amer. Math. Soc. 103 (1988), 1175-1178
MSC: Primary 42B20
MathSciNet review: 955003
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Singular integrals with kernels of the form $ K(x,y)$ where $ K$ satisfies conditions to be a bounded singular integral operator in each of its variables have been much studied lately. In this paper we use the classical method of rotations to give a proof that kernels of the form $ K(x,y) = \Omega (x,y)/\vert x{\vert^n}\vert y{\vert^m}$ correspond to bounded singular integral operators.

References [Enhancements On Off] (What's this?)

  • [1] R. Coifman and C. Fefferman, Weighted norm inequalities for maximal functions and singular integrals, Studia Math. 51 (1974), 241-250. MR 0358205 (50:10670)
  • [2] R. Fefferman, Singular integrals on product $ {H^p}$-spaces, preprint.
  • [3] R. Fefferman and E. M. Stein, Singular integrals on product spaces, Adv. in Math. 45 (1982), 117-143. MR 664621 (84d:42023)
  • [4] E. M. Stein and G. Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton Univ. Press, Princeton, N. J., 1971. MR 0304972 (46:4102)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 42B20

Retrieve articles in all journals with MSC: 42B20

Additional Information

Article copyright: © Copyright 1988 American Mathematical Society

American Mathematical Society