Abstract
We prove the weighted endpoint estimates for some multilinear operators related to certain singular integral operators on some Hardy and Herz type Hardy spaces.
Similar content being viewed by others
References
Chen, W., Hu, G.: Weak type (\(H^{1}\), \(L^{1}\)) estimate for multilinear singular integral operator. Adv. Math. (China) 30, 63–69 (2001)
Cohen, J.: A sharp estimate for a multilinear singular integral on \(R^{n}\). Indiana Univ. Math. J. 30, 693–702 (1981)
Cohen, J., Gosselin, J.: On multilinear singular integral operators on \(R^{n}\). Stud. Math. 72, 199–223 (1982)
Cohen, J., Gosselin, J.: A BMO estimate for multilinear singular integral operators. Ill. J. Math. 30, 445–465 (1986)
Coifman, R., Meyer, Y.: Wavelets, Calderón-Zygmund and Multilinear Operators. Cambridge Studies in Advanced Math., vol. 48. Cambridge Univ. Press, Cambridge (1997)
Coifman, R., Rochberg, R., Weiss, G.: Factorization theorems for Hardy spaces in several variables. Ann. Math. 103, 611–635 (1976)
Ding, Y., Lu, S.Z.: Weighted boundedness for a class rough multilinear operators. Acta Math. Sin. 17, 517–526 (2001)
Garcia-Cuerva, J.: Hardy spaces and Beurling algebras. J. Lond. Math. Soc. 39, 499–513 (1989)
Garcia-Cuerva, J., Herrero, M.L.: A theory of Hardy spaces associated to the Herz spaces. Proc. Lond. Math. Soc. 69, 605–628 (1994)
Garcia-Cuerva, J., Rubio de Francia, J.L.: Weighted Norm Inequalities and Related Topics. North-Holland, Amsterdam (1985)
Harboure, E., Segovia, C., Torra, J.L.: Boundedness of commutators of fractional and singular integrals for the extreme values of \(p\). Ill. J. Math. 41, 676–700 (1997)
Liu, L.Z.: Boundedness of multilinear operator related to generalized fractional singular integral operator for the extreme cases. Integral Transforms Spec. Funct. 24, 201–220 (2013)
Liu, L.Z.: Weighted boundedness of multilinear operators associated to Riesz transforms of Schrödinger operator for the extreme cases. J. Pseud.-Differ. Oper. Appl. 4, 393–412 (2013)
Liu, L.Z.: Boundedness of multilinear singular integral operators satisfying a variant of Hörmander’s condition and mean oscillation. Anal. Math. Phys. 6, 345–363 (2016)
Lu, S.Z., Yang, D.C.: The decomposition of the weighted Herz spaces and its applications. Sci. China Ser. A 38, 147–158 (1995)
Lu, S.Z., Yang, D.C.: The weighted Herz type Hardy spaces and its applications. Sci. China Ser. A 38, 662–673 (1995)
Stein, E.M.: Harmonic Analysis: Real Variable Methods, Orthogonality and Oscillatory Integrals. Princeton Univ. Press, Princeton (1993)
Zhang, M.J., Guo, Y.F.: Weighted boundedness of multilinear singular integral operator with general kernels for the extreme cases. J. Inequal. Appl. 341, 1 (2014)
Acknowledgements
The author would like to express his deep gratitude to the referee for his/her valuable comments and suggestions.
Project supported by the Scientific Research Fund of Hunan Provincial Education Departments (15C1236).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Chen, D. Weighted Hardy Type Spaces Estimates of Multilinear Singular Integral Operators for the Extreme Cases. Acta Appl Math 154, 167–187 (2018). https://doi.org/10.1007/s10440-017-0139-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10440-017-0139-9