Geodesic
Maximal Operator for the Higher Order Calderón Commutator
Canadian journal of mathematics, Tome 72 (2020) no. 5, pp. 1386-1422

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper, we investigate the weighted multilinear boundedness properties of the maximal higher order Calderón commutator for the dimensions larger than two. We establish all weighted multilinear estimates on the product of the $L^{p}(\mathbb{R}^{d},w)$ space, including some peculiar endpoint estimates of the higher dimensional Calderón commutator.
DOI : 10.4153/S0008414X19000476
Mots-clés : Multilinear, Calderón commutator, maximal operator, weighted space 
Lai, Xudong. Maximal Operator for the Higher Order Calderón Commutator. Canadian journal of mathematics, Tome 72 (2020) no. 5, pp. 1386-1422. doi: 10.4153/S0008414X19000476
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[1] Bergh, J. and Löfström, J., Interpolation spaces. An introduction. Grundlehren der Mathematischen Wissenschaften, 223, Springer-Verlag, Berlin, New York, 1976. Google Scholar | DOI

[2] Calderón, A.-P., Commutators of singular integral operators. Proc. Natl Acad. Sci. USA 53(1965), 1092–1099. https://doi.org/10.1073/pnas.53.5.1092 Google Scholar PubMed | DOI

[3] Calderón, A.-P., Cauchy integrals on Lipschitz curves and related operators. Proc. Natl Acad. Sci. USA 74(1977), 1324–1327. https://doi.org/10.1073/pnas.74.4.1324 Google Scholar PubMed | DOI

[4] Calderón, A.-P., Commutators, singular integrals on Lipschitz curves and application. In: Proceedings of the International Congress of Mathematicians (Helsinki, 1978). Acad. Sci. Fennica, Helsinki, 1980, pp. 85–96. Google Scholar

[5] Calderón, C. P., On commutators of singular integrals. Studia Math. 53(1975), 139–174. https://doi.org/10.4064/sm-53-2-139-174 Google Scholar | DOI

[6] Coifman, R. and Meyer, Y., On commutators of singular integral and bilinear singular integrals. Trans. Amer. Math. Soc. 212(1975), 315–331. https://doi.org/10.2307/1998628 Google Scholar | DOI

[7] Coifman, R. and Meyer, Y., Au delà des opérateurs pseudo-différentiels. Astérisque, 57, Société Mathématique de France, Paris, 1978. Google Scholar

[8] Christ, M. and Journé, J. L., Polynomial growth estimates for multilinear singular integral operators. Acta Math. 159(1987), 51–80. https://doi.org/10.1007/BF02392554 Google Scholar | DOI

[9] David, G. and Semmes, S., Strong A weights, Sobolev inequalities and quasiconformal mappings. In: Analysis and partial differential equations. Lecture Notes in Pure and Appl. Math., 122, Dekker, New York, 1990, pp. 101–111. Google Scholar

[10] Ding, Y. and Lai, X., Weak type (1, 1) bound criterion for singular integral with rough kernel and its applications. Trans. Amer. Math. Soc. 371(2019), no. 3, 1649–1675. https://doi.org/10.1090/tran/7346 Google Scholar | DOI

[11] Duong, X., Grafakos, L., and Yan, L., Multilinear operators with non-smooth kernels and commutators of singular integrals. Trans. Amer. Math. Soc. 362(2010), no. 4, 2089–2113. https://doi.org/10.1090/S0002-9947-09-04867-3 Google Scholar | DOI

[12] Duong, X., Gong, R., Grafakos, L., Li, J., and Yan, L., Maximal operator for multilinear singular integrals with non-smooth kernels. Indiana Univ. Math. J. 58(2009), no. 6, 2517–2541. https://doi.org/10.1512/iumj.2009.58.3803 Google Scholar | DOI

[13] Fefferman, C., Recent progress in classical Fourier analysis. In: Proceedings of the International Congress of Mathematicians (Vancouver, BC, 1974). Canad. Math. Congress, Montreal, Que., 1975, pp. 95–118. Google Scholar

[14] Fong, P. W., Smoothness properties of symbols, Calderón commutators and generalizations. Thesis (Ph.D.), Cornell University, 2016. Google Scholar

[15] García-Cuerva, J. and Rubio De Francia, J., Weighted norm inequalities and related topics. North-Holland Math. Studies, 116, North-Holland, Amsterdam, 1985. Google Scholar

[16] Grafakos, L., Classic Fourier analysis. Third ed., Graduate Texts in Mathematics, 249, Springer, New York, 2014. https://doi.org/10.1007/978-1-4939-1194-3 Google Scholar

[17] Grafakos, L., Modern Fourier analysis. Third ed., Graduate Texts in Mathematics, 250, Springer, New York, 2014. https://doi.org/10.1007/978-1-4939-1230-8 Google Scholar

[18] Grafakos, L., Liu, L., and Yang, D., Multiple-weighted norm inequalities for maximal multi-linear singular integrals with non-smooth kernels. Proc. Roy. Soc. Edinburgh Sect. A 141(2011), no. 4, 755–775. https://doi.org/10.1017/S0308210509001383 Google Scholar | DOI

[19] Hadžić, M., Seeger, A., Smart, C. K., and Street, B., Singular integrals and a problem on mixing flows. Ann. Inst. H. Poincare Anal. Non Lineaire. 35(2018), no. 4, 921–943. Google Scholar | DOI

[20] Journé, J. L., Calderón–Zygmund operators, pseudodifferential operators and the Cauchy integral of Calderón. Lecture Notes in Mathematics, 994, Springer-Verlag, Berlin, 1983. https://doi.org/10.1007/BFb0061458 Google Scholar | DOI

[21] Lai, X., Multilinear estimates for Calderón commutators. Int. Math. Res. Not. IMRN. (2018). https://doi.org/10.1093/imrn/rny197 Google Scholar | DOI

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

[23] Léger, F., A new approach to bounds on mixing. Math. Models Methods Appl. Sci. 28(2018), no. 5, 829–849. https://doi.org/10.1142/S0218202518500215 Google Scholar | DOI

[24] Meyer, Y. and Coifman, R., Wavelets. Calderón–Zygmund and multilinear operators. Cambridge Studies in Advanced Mathematics, 48, Cambridge University Press, Cambridge, 1997. Google Scholar

[25] Seeger, A., Smart, C. K., and Street, B., Multilinear singular integral forms of Christ-Journé type. Mem. Amer. Math. Soc. 257(2019), no. 1231. Google Scholar

[26] Stein, E. M., Singular integrals and differentiability properties of functions. Princeton Mathematical Series, 30, Princeton University Press, Princeton, NJ, 1970. Google Scholar

[27] Stein, E. M. and Weiss, G., Interpolation of operators with change of measures. Trans. Amer. Math. Soc. 87(1958), 159–172. https://doi.org/10.2307/1993094 Google Scholar | DOI

[28] Stein, E. M. and Weiss, G., Introduction to Fourier analysis on Euclidean spaces. Princeton Mathematical Series, 32, Princeton University Press, Princeton, NJ, 1971. Google Scholar

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