Estimates for the maximal bilinear singular integral operators

Springer Science and Business Media LLC - Tập 31 - Trang 847-862 - 2015
Guo En Hu1
1Department of Applied Mathematics, Zhengzhou Information Science and Technology Institute, Zhengzhou, P. R. China

Tóm tắt

In this paper, the behavior on the product of Lebesgue spaces is considered for the maximal operators associated with the bilinear singular integral operators whose kernels satisfy certain minimal regularity conditions.

Tài liệu tham khảo

Coifman, R. R., Meyer, Y.: On commutators of singular integrals and bilinear singular integrals. Trans. Amer. Math. Soc., 212, 315–331 (1975) Coifman, R. R., Meyer, Y.: Au delà des opérateurs pseudo-différentiels. Astériaque, 57, 1–185 (1978) Grafakos, L.: Estimates for maximal singular integral operator. Colloquium Math., 96, 167–177 (2003) Grafakos, L., Torres, R.: Multilinear Calderón-Zygmund theory. Adv. Math., 165, 124–164 (2002) Grafakos, L., Torres, R.: Maximal operator and weighted norm inequalities for multilinear singular integrals. Indiana Univ. Math. J., 51, 1261–1276 (2002) Hu, G., Yang, Da., Yang, Do.: Estimates for maximal singular integral operators on homogeneous type. J. Math. Soc. Japan, 59, 323–349 (2007) John, F.: Quasi-isometric Mappings. In: 1965 Seminari, Anal. Alg. Geom. e Topol., vol. 2, Ist. Naz. Alta Mat., Ediz. Cremonese, Rome, 1962/63, 462–473 Kurtz, D. S., Wheeden, R. L.: Results on weighted norm inequalities for multipliers. Tans. Amer. Math. Soc., 255, 343–362 (1979) Lerner, A., Ombrossi, S., Pérez, C., et al.: New maximal functions and multiple weights for the multilinear Calderón-Zygmund theorey. Adv. Math., 220, 1222–1264 (2009) Lu, G., Zhang, P.: Multilinear Calderón-Zygmund operators with kernels of Dinis type and applications. Nonlinear Anal. ATA, 107, 92–117 (2014) Maldonado, D., Naibo, V.: Weighted norm inequalities for paraproducts and bilinear pseudodifferential operators with mild regularity. J. Fourier Anal. Appl., 15, 218–261 (2009) Pérez, C., Torres, R. H.: Minimal regularity conditions for the end-point estimates of bilinear Calderón-Zygmund operators. Proc. Amer. Math. Soc. Ser. B, 1, 1–13 (2014) Strömberg, J. O.: Bounded mean oscillation with Orlicz norms and duality of Hardy spaces. Indiana Univ. Math. J., 28, 511–544 (1979)