On rough singular integrals along real-analytic submanifolds

References

[1] H. Al-Qassem and Y. Pan, On certain estimates for Marcinkiewicz integrals and extrapolation, Collect. Math. 60 (2009), no. 2, 123–145. 10.1007/BF03191206Search in Google Scholar

[2] H. M. Al-Qassem, Maximal operators related to block spaces, Kodai Math. J. 28 (2005), no. 3, 494–510. 10.2996/kmj/1134397763Search in Google Scholar

[3] H. M. Al-Qassem, On the boundedness of maximal operators and singular operators with kernels in L⁢(log⁡L)α⁢(𝐒n-1), J. Inequal. Appl. 2006 (2006), Article ID 96732. 10.1155/JIA/2006/96732Search in Google Scholar

[4] A. Al-Salman, On maximal functions with rough kernels in L⁢(log⁡L)1/2⁢(𝕊n-1), Collect. Math. 56 (2005), no. 1, 47–56. Search in Google Scholar

[5] A. Al-Salman, On a class of singular integral operators with rough kernels, Canad. Math. Bull. 49 (2006), no. 1, 3–10. 10.4153/CMB-2006-001-9Search in Google Scholar

[6] A. Al-Salman, Rough maximal functions supported by subvarieties, J. Operator Theory 59 (2008), no. 2, 263–275. Search in Google Scholar

[7] A. Al-Salman and Y. Pan, Singular integrals with rough kernels in L⁢log⁡L⁢(𝐒n-1), J. London Math. Soc. (2) 66 (2002), no. 1, 153–174. 10.1112/S0024610702003241Search in Google Scholar

[8] A. Benedek and R. Panzone, The space Lp, with mixed norm, Duke Math. J. 28 (1961), 301–324. 10.1215/S0012-7094-61-02828-9Search in Google Scholar

[9] A. P. Calderón and A. Zygmund, On singular integrals, Amer. J. Math. 78 (1956), 289–309. 10.1090/pspum/010Search in Google Scholar

[10] L.-K. Chen and H. Lin, A maximal operator related to a class of singular integrals, Illinois J. Math. 34 (1990), no. 1, 120–126. 10.1215/ijm/1255988497Search in Google Scholar

[11] M. Christ, A. Nagel, E. M. Stein and S. Wainger, Singular and maximal Radon transforms: analysis and geometry, Ann. of Math. (2) 150 (1999), no. 2, 489–577. 10.2307/121088Search in Google Scholar

[12] R. R. Coifman and G. Weiss, Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc. 83 (1977), no. 4, 569–645. 10.1515/9781400827268.295Search in Google Scholar

[13] W. C. Connett, Singular integrals near L1, Harmonic Analysis in Euclidean Spaces. Part 1 (Williamstown 1978), Proc. Sympos. Pure Math. 35, American Mathematical Society, Providence (1979), 163–165. 10.1090/pspum/035.1/545253Search in Google Scholar

[14] J. Duoandikoetxea and J. L. Rubio de Francia, Maximal and singular integral operators via Fourier transform estimates, Invent. Math. 84 (1986), no. 3, 541–561. 10.1007/BF01388746Search in Google Scholar

[15] D. Fan, K. Guo and Y. Pan, Singular integrals with rough kernels along real-analytic submanifolds in 𝐑n, Integral Equations Operator Theory 33 (1999), no. 1, 8–19. 10.1090/S0002-9947-02-03175-6Search in Google Scholar

[16] D. Fan, K. Guo and Y. Pan, Singular integrals with rough kernels along real-analytic submanifolds in 𝐑3, Trans. Amer. Math. Soc. 355 (2003), no. 3, 1145–1165. 10.1090/S0002-9947-02-03175-6Search in Google Scholar

[17] D. Fan and Y. Pan, Singular integral operators with rough kernels supported by subvarieties, Amer. J. Math. 119 (1997), no. 4, 799–839. 10.1353/ajm.1997.0024Search in Google Scholar

[18] R. Fefferman, A note on singular integrals, Proc. Amer. Math. Soc. 74 (1979), no. 2, 266–270. 10.1090/S0002-9939-1979-0524298-3Search in Google Scholar

[19] L. Hörmander, The Analysis of Linear Partial Differential Operators. I, Springer, Berlin, 1983. Search in Google Scholar

[20] Y. S. Jiang and S. Z. Lu, Lp boundedness of a class of maximal singular integral operators, Acta Math. Sinica 35 (1992), no. 1, 63–72. Search in Google Scholar

[21] F. Liu, S. Mao and H. Wu, On rough singular integrals related to homogeneous mappings, Collect. Math. 67 (2016), no. 1, 113–132. 10.1007/s13348-015-0155-xSearch in Google Scholar

[22] D. Müller, Singular kernels supported by homogeneous submanifolds, J. Reine Angew. Math. 356 (1985), 90–118. 10.1515/crll.1985.356.90Search in Google Scholar

[23] J. Namazi, A singular integral, Proc. Amer. Math. Soc. 96 (1986), no. 3, 421–424. 10.1090/S0002-9939-1986-0822432-2Search in Google Scholar

[24] Y. Pan, Boundedness of oscillatory singular integrals on Hardy spaces. II, Indiana Univ. Math. J. 41 (1992), no. 1, 279–293. 10.1512/iumj.1992.41.41016Search in Google Scholar

[25] D. H. Phong and E. M. Stein, Singular integrals related to the Radon transform and boundary value problems, Proc. Natl. Acad. Sci. USA 80 (1983), no. 24, 7697–7701. 10.1073/pnas.80.24.7697Search in Google Scholar PubMed PubMed Central

[26] D. H. Phong and E. M. Stein, Hilbert integrals, singular integrals, and Radon transforms. I, Acta Math. 157 (1986), no. 1–2, 99–157. 10.1007/BF02392592Search in Google Scholar

[27] S. Sato, Estimates for singular integrals and extrapolation, Studia Math. 192 (2009), no. 3, 219–233. 10.4064/sm192-3-2Search in Google Scholar

[28] E. M. Stein, Problems in harmonic analysis related to curvature and oscillatory integrals, Proceedings of the International Congress of Mathematicians (Berkeley 1986), American Mathematical Society, Providence (1987), 196–221. Search in Google Scholar

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

[30] H. Xu, D. S. Fan and M. Wang, Some maximal operators related to families of singular integral operators, Acta Math. Sin. (Engl. Ser.) 20 (2004), no. 3, 441–452. 10.1007/s10114-004-0366-7Search in Google Scholar