We prove the 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 (cf. below). The importance of these perturbations lies in potential theoretic applications (cf. [2,4]).
@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://www.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://www.numdam.org/item/ASNSP_2009_5_8_3_583_0/ LA - en ID - ASNSP_2009_5_8_3_583_0 ER -
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://www.numdam.org/item/ASNSP_2009_5_8_3_583_0/
[1] Polynomial growth estimates for multilinear singular operators, Acta Math. 159 (1987), 51–80. | MR | Zbl
and ,[2] Some new function spaces and their applications in harmonic analysis, J. Funct. Anal. 62 (1985), 302–335. | MR
, and ,[3] Poisson semigroups and singular integrals, Proc. Amer. Math. Soc. 97 (1986), 41–48. | MR | Zbl
,[4] Maximal and singular integral operators via Fourier transform estimates, Invent. Math. 84 (1986), 541–561. | EuDML | MR | Zbl
and ,[5] An extrapolation theorem in the theory of weights, Proc. Amer. Math. Soc. 87 (1983), 422–426. | MR | Zbl
,[6] “Harmonic Analysis Real-Variable Methods, Orthogonality, and Oscillatory Integrals”, Princeton University Press, 1993. | MR | Zbl
,[7] Singular integrals and potential theory. Milan J. Math. 75 (2007), 1–60. | MR | Zbl
,[8] Singular integrals and potential theory (II), Milan J. Math. 76 (2008), 419–429. | MR | Zbl
,