Some estimates of multi-sublinear operators and commutators on mixed $$\lambda $$-central Morrey spaces

Alvarez, J., Guzmán-Partida, M., Lakey, J.: Spaces of bounded $$\lambda $$-central mean oscillation, Morrey spaces, and $$\lambda $$-central Carleson measures. Collect. Math. 51, 1–47 (2000)

Antonic, N., Ivec, I.: On the Hörmander–Mihlin theorem for mixed-norm Lebesgue spaces. Math. Anal. Appl. 433, 176–199 (2016)

Benedek, A., Panzone, R.: The space $$L^{p}$$, with mixed norm. Duke Math. 28, 301–324 (1961)

Coifman, R., Meyer, Y.: On commutators of singular integrals and bilinear singular integrals. Trans. Am. Math. Soc. 212, 315–331 (1975)

Coifman, R., Meyer, Y.: Commutateurs d’intégrales singuliéres et opérateurs multilinéaires. Ann. Inst. Fourier Grenoble 28, 177–202 (1978)

Chen, X., Xue, Q.: Weighted estimates for a class of multilinear fractional type operators. J. Math. Anal. Appl. 362, 355–373 (2010)

Dong, H., Kim, D., Phan, T.: Boundary Lebesgue mixed-norm estimates for non-stationary Stokes systems with VMO coefficients. Commun. PDE 47(8), 1700–1731 (2022)

Fu, Z., Lin, Y., Lu, S.: $$\lambda $$-central $${{\rm BMO}}$$ estimates for commutators of singular integral operators with rough kernels. Acta Math. Sin. 24(3), 373–386 (2008)

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)

Ismayilova, A., Isayev, F.: Multi-sublinear operators generated by multilinear Calderón–Zygmund operators on product generalized Morrey spaces. Trans. Natl. Acad. Sci. Azerbaijan Ser. Phys. Tech. Math. Sci. Issue Math. 40(4), 110–117 (2020)

Kenig, C.: On the local and global well-posedness theory for the KP-I equation. Ann. Inst. Henri Poincaré Anal. Non Linéaire 21, 827–838 (2004)

Kenig, C., Stein, E.: Multilinear estimates and fractional integration. Math. Res. Lett. 6, 1–15 (1999)

Kim, D.: Elliptic and parabolic equations with measurable coefficients in $$L^{p}$$-spaces with mixed norms. Methods Appl. Anal. 15, 437–468 (2008)

Krylov, N.: Parabolic equations with $${{\rm VMO}}$$ coefficients in Sobolev spaces with mixed norms. J. Funct. Anal. 250, 521–558 (2007)

Lin, Y., Lu, S.: Multilinear Calderón–Zygmund operator on Morrey type spaces. Anal. Theory Appl. 22(4), 387–400 (2006)

Lerner, A., Ombrosi, S., Pérez, C., Torres, R., Trujillo-González, R.: New maximal functions and multiple weights for the multilinear Calderón–Zygmund theory. Adv. Math. 220, 1222–1264 (2009)

Liu, R., Liu, F., Wu, H.: Mixed radial-angular integrability for rough singular integrals and maximal operators. Proc. Am. Math. Soc. 148(9), 3943–3956 (2020)

Liu, R., Liu, F., Wu, H.: On the mixed radial-angular integrability of Marcinkiewicz integrals with rough kernels. Acta Math. Sci. Ser. B (Engl. Ed.) 41(1), 241–256 (2021)

Liu, R., Wu, H.: Rough singular integrals and maximal operator with radial-angular integrability. Proc. Am. Math. Soc. 150(3), 1141–1151 (2022)

Lu, W., Zhou, J.: Fractional integral operators on the mixed $$\lambda $$-central Morrey spaces (2022). arXiv:2208.07356

Morrey, C.: On the solutions of quasi-linear elliptic partial differential equations. Trans. Am. Math. Soc. 43, 126–166 (1938)

Moen, K.: Weighted inequalities for multilinear fractional integral operators. Collect. Math. 60, 213–238 (2009)

Nogayama, T.: Mixed Morrey spaces. Positivity 23(4), 961–1000 (2019)

Nogayama, T.: Boundedness of commutators of fractional integral operators on mixed Morrey spaces. Integral Transform. Spec. Funct. 30(10), 790–816 (2019)

Pérez, C., Pradolini, G., Torres, R., Trujillo-Gonzlez, R.: End-point estimates for iterated commutators for multilinear singular integrals. Bull. Lond. Math. Soc. 46, 26–42 (2014)

Shi, Y., Tao, X.: Some multi-sublinear operators on generalized Morrey spaces with non-doubling measures. J. Korean Math. Soc. 49(5), 907–925 (2012)

Si, Z., Xue, Q.: $$\lambda $$-central $${{\rm BMO}}$$ estimates for commutators of multilinear maximal operators. Acta. Math. Sin. Engl. Ser. 29(4), 729–742 (2013)

Si, Z.: $$\lambda $$-central $${{\rm BMO}}$$ estimates for multilinear commutators of fractional integrals. Acta Math. Sin. Engl. Ser. 26, 2093–2108 (2010)

Tao, X., Shi, Y.: Multilinear commutators of Calderón–Zygmund operator on $$\lambda $$-central Morrey spaces. Adv. Math. (China) 40, 47–59 (2011)

Tao, X., Wu, Y.: Boundedness for the multi-commutators of Calderón–Zygmund operators. J. Math. Inequal. 6(4), 655–672 (2012)

Wei, M.: Multi-sublinear operators and their commutators on product generalized mixed Morrey spaces (2022). arXiv:2203.04720v1 [math.FA]

Xue, Q.: Weighted estimates for the iterated commutators of multilinear maximal and fractional type operators. Stud. Math. 217(2), 97–122 (2013)

Yu, X., Tao, X.: Boundedness for a class of generalized commutators on $$\lambda $$-central Morrey spaces. Acta Math. Sin. 29(10), 1917–1926 (2013)