Maximal singular integrals
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Volume 8 (2009) no. 3, p. 583-612
We prove the L p boundedness of the maximal operators attached to the singular kernels introduced in [1]. These kernels are obtained by multiplying (pointwise) a classical convolution Calderon-Zygmund kernel with the perturbing factor [a] x,y (cf. below). The importance of these perturbations lies in potential theoretic applications (cf. [2,4]).
Classification:  42B20,  42B25 
@article{ASNSP_2009_5_8_3_583_0,
     author = {Varopoulos, Nicolas},
     title = {Maximal singular integrals},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 8},
     number = {3},
     year = {2009},
     pages = {583-612},
     zbl = {1206.42018},
     mrnumber = {2581427},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2009_5_8_3_583_0}
}

Varopoulos, Nicolas. Maximal singular integrals. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Volume 8 (2009) no. 3, pp. 583-612. http://www.numdam.org/item/ASNSP_2009_5_8_3_583_0/

[1] M. Christ and J.-L. Journé, Polynomial growth estimates for multilinear singular operators, Acta Math. 159 (1987), 51–80. | MR 906525 | Zbl 0645.42017

[2] R. R. Coifman, Y. Meyer and E. M. Stein, Some new function spaces and their applications in harmonic analysis, J. Funct. Anal. 62 (1985), 302–335. | MR 791851

[3] B. E. Dahlberg, Poisson semigroups and singular integrals, Proc. Amer. Math. Soc. 97 (1986), 41–48. | MR 831384 | Zbl 0595.31009

[4] J. Duandikoetxea and J. L. Rubio De Francia, Maximal and singular integral operators via Fourier transform estimates, Invent. Math. 84 (1986), 541–561. | MR 837527 | Zbl 0568.42012

[5] J. Garcia-Cuerva, An extrapolation theorem in the theory of A p weights, Proc. Amer. Math. Soc. 87 (1983), 422–426. | MR 684631 | Zbl 0542.41011

[6] E. M. Stein, “Harmonic Analysis Real-Variable Methods, Orthogonality, and Oscillatory Integrals”, Princeton University Press, 1993. | MR 1232192 | Zbl 0821.42001

[7] N. Th. Varopoulos, Singular integrals and potential theory. Milan J. Math. 75 (2007), 1–60. | MR 2371537 | Zbl 1139.42003

[8] N. Th. Varopoulos, Singular integrals and potential theory (II), Milan J. Math. 76 (2008), 419–429. | MR 2465998 | Zbl 1173.42007