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Oscillatory singular integral operators with Hölder class kernels on Hardy spaces

  • Yibiao Pan ORCID logo EMAIL logo
Published/Copyright: December 16, 2018

Abstract

A sharp logarithmic bound is established for the H1-norm of oscillatory singular integrals with quadratic phases and Hölder class kernels. Prior results had relied on a C1-assumption on the kernel.

MSC 2010: 42B20; 42B35

Communicated by Christopher D. Sogge


References

[1] H. Al-Qassem, L. Cheng and Y. Pan, Logarithmic bounds for oscillatory singular integrals on Hardy spaces, J. Funct. Spaces 2016 (2016), Article ID 1570109. 10.1155/2016/1570109Search in Google Scholar

[2] R. Coifman, A real variable characterization of Hp, Studia Math. 51 (1974), 269–274. 10.4064/sm-51-3-269-274Search in Google Scholar

[3] D. Fan and Y. Pan, Singular integral with rough kernels supported by subvarieties, Amer. J. Math. 119 (1997), 799–839. 10.1353/ajm.1997.0024Search in Google Scholar

[4] C. Fefferman and E. M. Stein, Hp spaces of several variables, Acta Math. 129 (1972), 137–193. 10.1007/BF02392215Search in Google Scholar

[5] L. Grafakos, Classical and Modern Fourier Analysis, Pearson Education, Upper Saddle River, 2004. Search in Google Scholar

[6] Y. Hu and Y. Pan, Boundedness of oscillatory singular integrals on Hardy spaces, Ark. Mat. 30 (1992), 311–320. 10.1007/BF02384877Search in Google Scholar

[7] D. Phong and E. M. Stein, Hilbert integrals, singular integrals, and Radon transforms. I, Acta. Math. 157 (1986), 99–157. 10.1007/BF02392592Search in Google Scholar

[8] F. Ricci and E. M. Stein, Harmonic analysis on nilpotent groups and singular integrals. I. Oscillatory integrals, J. Funct. Anal. 73 (1987), 179–194. 10.1016/0022-1236(87)90064-4Search in Google Scholar

[9] P. Sjölin, Convolution with oscillating kernels on Hp spaces, J. Lond. Math. Soc. (2) 23 (1981), 442–454. 10.1112/jlms/s2-23.3.441Search in Google Scholar

[10] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton University Press, Princeton, 1970. 10.1515/9781400883882Search in Google Scholar

[11] E. M. Stein, Oscillatory integrals in fourier analysis, Beijing Lectures in Harmonic Analysis, Ann. of Math. Stud. 112, Princeton University Press, Princeton (1986), 307–335. 10.1515/9781400882090-007Search in Google Scholar

[12] E. M. Stein, Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton University Press, Princeton, 1993. 10.1515/9781400883929Search in Google Scholar

Received: 2018-10-15
Published Online: 2018-12-16
Published in Print: 2019-03-01

© 2019 Walter de Gruyter GmbH, Berlin/Boston

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