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ESTIMATES FOR SINGULAR INTEGRALS ALONG SURFACES OF REVOLUTION

  • SHUICHI SATO (a1)
Abstract
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.

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References
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[2] A. P. Calderón and A. Torchinsky , ‘Parabolic maximal functions associated with a distribution’, Adv. Math. 16 (1975), 164.

[5] J. Duoandikoetxea and J. L. Rubio de Francia , ‘Maximal and singular integral operators via Fourier transform estimates’, Invent. Math. 84 (1986), 541561.

[9] S. Hofmann , ‘Weighted norm inequalities and vector valued inequalities for certain rough operators’, Indiana Univ. Math. J. 42 (1993), 114.

[10] W. Kim , S. Wainger , J. Wright and S. Ziesler , ‘Singular integrals and maximal functions associated to surfaces of revolution’, Bull. London Math. Soc. 28 (1996), 291296.

[12] J. Namazi , ‘On a singular integral’, Proc. Amer. Math. Soc. 96 (1986), 421424.

[13] N. Rivière , ‘Singular integrals and multiplier operators’, Ark. Mat. 9 (1971), 243278.

[14] S. Sato , ‘Estimates for singular integrals and extrapolation’, Studia Math. 192 (2009), 219233.

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Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
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