A singular integral
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- by Javad Namazi PDF
- Proc. Amer. Math. Soc. 96 (1986), 421-424 Request permission
Abstract:
In this paper we show that if $K(x) = \Omega (x)/{\left | x \right |^n}$ is a Calderón-Zygmund kernel, where $\Omega \in {L^q}({S^{n - 1}})$ for some $1 < q \leq \infty$, and $b$ is a radial bounded function, then $b(x)K(x)$ is the kernel of a convolution operator which is bounded on ${L^p}({R^n})$ for $1 < p < \infty$ and $n \geq 2$.References
- R. Fefferman, A note on singular integrals, Proc. Amer. Math. Soc. 74 (1979), no. 2, 266–270. MR 524298, DOI 10.1090/S0002-9939-1979-0524298-3 Javad Namazi, On a singular integral, Thesis reprint.
- Elias M. Stein, Singular integrals and differentiability properties of functions, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J., 1970. MR 0290095
- Elias M. Stein and Guido Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton Mathematical Series, No. 32, Princeton University Press, Princeton, N.J., 1971. MR 0304972
Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 96 (1986), 421-424
- MSC: Primary 42B20
- DOI: https://doi.org/10.1090/S0002-9939-1986-0822432-2
- MathSciNet review: 822432