On weighted compactness of commutators of bilinear maximal Calderón–Zygmund singular integral operators

References

[1] F. Beatrous and S.-Y. Li, On the boundedness and compactness of operators of Hankel type, J. Funct. Anal. 111 (1993), no. 2, 350–379. 10.1006/jfan.1993.1017Search in Google Scholar

[2] A. Bényi, W. Damián, K. Moen and R. H. Torres, Compact bilinear commutators: The weighted case, Michigan Math. J. 64 (2015), no. 1, 39–51. 10.1307/mmj/1427203284Search in Google Scholar

[3] A. Bényi, W. Damián, K. Moen and R. H. Torres, Compactness properties of commutators of bilinear fractional integrals, Math. Z. 280 (2015), no. 1–2, 569–582. 10.1007/s00209-015-1437-4Search in Google Scholar

[4] A. Bényi and R. H. Torres, Compact bilinear operators and commutators, Proc. Amer. Math. Soc. 141 (2013), no. 10, 3609–3621. 10.1090/S0002-9939-2013-11689-8Search in Google Scholar

[5] R. Bu and J. Chen, Compactness for the commutators of multilinear singular integral operators with non-smooth kernels, Appl. Math. J. Chinese Univ. Ser. B 34 (2019), no. 1, 55–75. 10.1007/s11766-019-3501-zSearch in Google Scholar

[6] M. Cao, A. Olivo and K. Yabuta, Extrapolation for multilinear compact operators and applications, preprint (2020), https://arxiv.org/abs/2011.13191. 10.1090/tran/8645Search in Google Scholar

[7] M. Cao, A. Olivo and K. Yabuta, Weighted interpolation for multilinear compact operators, preprint (2020). Search in Google Scholar

[8] X. Chen, Weighted estimates for the maximal operator of a multilinear singular integral, Bull. Pol. Acad. Sci. Math. 58 (2010), no. 2, 129–135. 10.4064/ba58-2-4Search in Google Scholar

[9] Y. Chen and Y. Ding, Compactness characterization of commutators for Littlewood–Paley operators, Kodai Math. J. 32 (2009), no. 2, 256–323. 10.2996/kmj/1245982907Search in Google Scholar

[10] Y. Chen, Y. Ding and X. Wang, Compactness for commutators of Marcinkiewicz integrals in Morrey spaces, Taiwanese J. Math. 15 (2011), no. 2, 633–658. 10.11650/twjm/1500406226Search in Google Scholar

[11] Y. Chen and Y. Ding, Compactness of commutators of singular integral operations with variable kernel, Chinese Ann. Math. Ser. A 30 (2009), no. 2, 201–212. Search in Google Scholar

[12] R. R. Coifman and C. Fefferman, Weighted norm inequalities for maximal functions and singular integrals, Studia Math. 51 (1974), 241–250. 10.4064/sm-51-3-241-250Search in Google Scholar

[13] R. R. Coifman, R. Rochberg and G. Weiss, Factorization theorems for Hardy spaces in several variables, Ann. of Math. (2) 103 (1976), no. 3, 611–635. 10.2307/1970954Search in Google Scholar

[14] H. O. Cordes, On compactness of commutators of multiplications and convolutions, and boundedness of pseudodifferential operators, J. Funct. Anal. 18 (1975), 115–131. 10.1016/0022-1236(75)90020-8Search in Google Scholar

[15] Y. Ding, T. Mei and Q. Xue, Compactness of maximal commutators of bilinear Calderón–Zygmund singular integral operators, Some topics in Harmonic Analysis and Applications, Adv. Lect. Math. (ALM) 34, International Press, Somerville (2016), 163–175. Search in Google Scholar

[16] W. Guo, Y. Wen, H. Wu and D. Yang, On the compactness of oscillation and variation of commutators, Banach J. Math. Anal. 15 (2021), no. 2, Paper No. 37. 10.1007/s43037-021-00123-zSearch in Google Scholar

[17] T. Hytönen, Extrapolation of compactness on weighted spaces, preprint (2020), https://arxiv.org/abs/2003.01606v2. 10.4171/RMI/1325Search in Google Scholar

[18] T. Hytönen and S. Lappas, Extrapolation of compactness on weighted spaces II: Off-diagonal and limited range estimates, preprint (2020), https://arxiv.org/abs/2006.15858v2. 10.4171/RMI/1325Search in Google Scholar

[19] T. Hytönen and S. Lappas, Extrapolation of compactness on weighted spaces III: Bilinear operators, preprint (2020), https://arxiv.org/abs/2012.10407. 10.4171/rmi/1325Search in Google Scholar

[20] S. G. Krantz and S.-Y. Li, Boundedness and compactness of integral operators on spaces of homogeneous type and applications. I, J. Math. Anal. Appl. 258 (2001), no. 2, 629–641. 10.1006/jmaa.2000.7402Search in Google Scholar

[21] S. G. Krantz and S.-Y. Li, Boundedness and compactness of integral operators on spaces of homogeneous type and applications. II, J. Math. Anal. Appl. 258 (2001), no. 2, 642–657. 10.1006/jmaa.2000.7403Search in Google Scholar

[22] A. K. Lerner, S. Ombrosi, C. Pérez, R. H. Torres and R. Trujillo-González, New maximal functions and multiple weights for the multilinear Calderón–Zygmund theory, Adv. Math. 220 (2009), no. 4, 1222–1264. 10.1016/j.aim.2008.10.014Search in Google Scholar

[23] F. Liu, S. Wang and Q. Xue, On oscillatory singular integrals and their commutators with non-convolutional Hölder class kernels, Banach J. Math. Anal. 15 (2021), no. 3, Paper No. 51. 10.1007/s43037-021-00138-6Search in Google Scholar

[24] C. Pérez and R. H. Torres, Sharp maximal function estimates for multilinear singular integrals, Harmonic Analysis at Mount Holyoke (South Hadley 2001), Contemp. Math. 320, American Mathematical Society, Providence (2003), 323–331. 10.1090/conm/320/05615Search in Google Scholar

[25] J. Tao, Q. Xue, D. Yang and W. Yuan, XMO and weighted compact bilinear commutators, J. Fourier Anal. Appl. 27 (2021), Article ID 60. 10.1007/s00041-021-09854-xSearch in Google Scholar

[26] R. Torres and Q. Xue, On compactness of commutators of multiplication and bilinear pseudodifferential operators and a new subspace of BMO, Rev. Mat. Iberoam. 36 (2020), no. 3, 939–956. 10.4171/rmi/1156Search in Google Scholar

[27] A. Uchiyama, On the compactness of operators of Hankel type, Tohoku Math. J. (2) 30 (1978), no. 1, 163–171. 10.2748/tmj/1178230105Search in Google Scholar

[28] S. Wang, Compactness of commutators of fractional integrals, Chinese Ann. Math. Ser. A 8 (1987), no. 4, 475–482. Search in Google Scholar

[29] Q. Xue, Weighted estimates for the iterated commutators of multilinear maximal and fractional type operators, Studia Math. 217 (2013), no. 2, 97–122. 10.4064/sm217-2-1Search in Google Scholar

[30] Q. Xue, K. Yabuta and J. Yan, Weighted Fréchet–Kolmogorov theorem and compactness of vector-valued multilinear operators, J. Geom. Anal. 31 (2021), no. 10, 9891–9914. 10.1007/s12220-021-00630-3Search in Google Scholar

[31] K. Yosida, Functional Analysis, Class. Math., Springer, Berlin, 1995. 10.1007/978-3-642-61859-8Search in Google Scholar