Maximal singular integrals
Varopoulos, Nicolas1, 2
1 I.U.F. Université Paris VI
2 Dipartimento di Matematica e Applicazioni, Università di Milano Bicocca, Via Cozzi, 53, 20125 Milano, Italia
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 8 (2009) no. 3, pp. 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
Varopoulos, Nicolas 1, 2

1 I.U.F. Université Paris VI
2 Dipartimento di Matematica e Applicazioni, Università di Milano Bicocca, Via Cozzi, 53, 20125 Milano, Italia 
@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},
     pages = {583--612},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 8},
     number = {3},
     year = {2009},
     mrnumber = {2581427},
     zbl = {1206.42018},
     language = {en},
     url = {http://archive.numdam.org/item/ASNSP_2009_5_8_3_583_0/}
}
TY  - JOUR
AU  - Varopoulos, Nicolas
TI  - Maximal singular integrals
JO  - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY  - 2009
SP  - 583
EP  - 612
VL  - 8
IS  - 3
PB  - Scuola Normale Superiore, Pisa
UR  - http://archive.numdam.org/item/ASNSP_2009_5_8_3_583_0/
LA  - en
ID  - ASNSP_2009_5_8_3_583_0
ER  - 
%0 Journal Article
%A Varopoulos, Nicolas
%T Maximal singular integrals
%J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
%D 2009
%P 583-612
%V 8
%N 3
%I Scuola Normale Superiore, Pisa
%U http://archive.numdam.org/item/ASNSP_2009_5_8_3_583_0/
%G en
%F ASNSP_2009_5_8_3_583_0
Varopoulos, Nicolas. Maximal singular integrals. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 8 (2009) no. 3, pp. 583-612. http://archive.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 | Zbl

[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

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

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

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

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

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

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