Besov Morrey spaces for Schrödinger operators with inverse–square potentials
Main Article Content
Abstract
Let be a Schrödinger operator with inverse square potential a|x|-2 on R3 , n \geq 3. The main aim of this paper is to develop the theory of new Besov–Morrey associated with L. These results generalize the corresponding results in [T. A. Bui. Besov and Triebel-Lizorkin spaces for Schrödinger operators with inverse–square potentials and applications, J. Diff. Eq., 269 (2020), 641-688].
Keywords
Inverse-square potential, Morrey spaces, Besov spaces
Article Details
References
Bui, T. A., Ancona, P. D., Duong, X. T., Li, J., & Ly, F. K. (2017). Weighted estimates for powers and smoothing estimates of Schrödinger operators with inverse–square potentials. Journal of Differential Equations, 262(3), 2771–2807. doi.org/10.1016/j.jde.2016.11.008
Bui, T. A. (2020). Besov and Triebel-Lizorkin spaces for Schrödinger operators with inverse–square potentials and applications. Journal of Differential Equations, 269, 641-688. doi.org/10.1016/j.jde.2019.12.016
Bui, H.-Q., Duong, X. T., Yan L. X. (2012). Calderón reproducing formulas and new Besov spaces associated with operators. Advances in Mathematics, 229(4), 2449–2502. https://doi.org/10.1016/j.aim.2012.01.005
Dao, N. A., Trong, N. N., & Truong, L. X. (2018). Besov-Morrey Spaces Associated to Hermite Operators and applications to Fractional Hermite Equations. Electronic Journal of Differential Equations, 2018(187), 1–14. https://digital.lib.ueh.edu.vn/handle/UEH/59707
Ifronika, Idris, M., Masta, A. A., & Gunawan, H. (2018). Generalized Hölder’s inequality in Morrey spaces. Matematički Vesnik, 70(4), 326–337. https://doi.org/10.48550/arXiv.1706.01659
Iwabuchi, T. (2018). The semigroup generated by the Dirichlet Laplacian of fractional order. Analysis of PDEs, 11(3), 683–703. https://doi.org/10.48550/arXiv.1712.05565
Keryacharian, G., & Petrushev, P. (2015). Heat kernel based decomposition of spaces of distributions in the framework of Dirichlet spaces, Transactions of the American Mathematical Society, 367(1), 121–189. https://doi.org/10.48550/arXiv.1210.6237
Kerkyacharia, G., Petrushev, P., Picard, D., & Xu, Y. (2009). Decomposition of Triebel-Lizorkin and Besov spaces in the context of Laguerre expansions. Journal of Functional Analysis, 256(4), 1137–1188. https://doi.org/10.1016/j.jfa.2008.09.015
Kozono, H., & Yamazaki, M. (1994). Semilinear heat equations and the Navier-Stokes equation with distributions in the new function spaces as initial data. Comm. Partial Differential Equations, 19(5–6), 959–1014. https://doi.org/10.1007/978-4-431-68413-8_10
Liskevich, V., & Sobol, Z. (2003). Estimates of integral kernels for semigroups associated with second order elliptic operators with singular coefficients. Potential Analysis, 18, 359–390. https://doi.org/10.1023/A:1021877025938
Anna Mazzucato, L. (2003). Besov-Morrey spaces: Function space theory and applications to nonlinear PDE. Transactions of the American Mathematical Society, 355, 1297–1364. DOI: 10.2307/1194896
Anna Mazzucato, L. (2003). Decomposition of Besov-Morrey spaces. Proceedings of the Conference on Harmonic Analysis. Contemp. Math. 320, Amer. Math. Soc., Providence, RI, 279–294. DOI: 10.1090/conm/320/05613
Morrey, C. B. (1938). On the solutions of quasi-linear elliptic partial differential equations. Transactions of the American Mathematical Society, 43, 126–166. https://doi.org/10.2307/1989904
Milman, P. D. & Semenov, Y. A. (2004). Global heat kernel bounds via desingularizing weights. Journal of Functional Analysis, 212, 373–398. https://doi.org/10.1016/j.jfa.2003.12.008
Trong, N. N., Truong, L. X., Dung, T. T., & Vo, H. N. (2020). Triebel-Lizorkin-Morrey spaces associated with Hermite operators. Revista Matemática Complutense, 33, 527–555. https://doi.org/10.1007/s13163-019-00314-1
Bui, T. A. (2020). Besov and Triebel-Lizorkin spaces for Schrödinger operators with inverse–square potentials and applications. Journal of Differential Equations, 269, 641-688. doi.org/10.1016/j.jde.2019.12.016
Bui, H.-Q., Duong, X. T., Yan L. X. (2012). Calderón reproducing formulas and new Besov spaces associated with operators. Advances in Mathematics, 229(4), 2449–2502. https://doi.org/10.1016/j.aim.2012.01.005
Dao, N. A., Trong, N. N., & Truong, L. X. (2018). Besov-Morrey Spaces Associated to Hermite Operators and applications to Fractional Hermite Equations. Electronic Journal of Differential Equations, 2018(187), 1–14. https://digital.lib.ueh.edu.vn/handle/UEH/59707
Ifronika, Idris, M., Masta, A. A., & Gunawan, H. (2018). Generalized Hölder’s inequality in Morrey spaces. Matematički Vesnik, 70(4), 326–337. https://doi.org/10.48550/arXiv.1706.01659
Iwabuchi, T. (2018). The semigroup generated by the Dirichlet Laplacian of fractional order. Analysis of PDEs, 11(3), 683–703. https://doi.org/10.48550/arXiv.1712.05565
Keryacharian, G., & Petrushev, P. (2015). Heat kernel based decomposition of spaces of distributions in the framework of Dirichlet spaces, Transactions of the American Mathematical Society, 367(1), 121–189. https://doi.org/10.48550/arXiv.1210.6237
Kerkyacharia, G., Petrushev, P., Picard, D., & Xu, Y. (2009). Decomposition of Triebel-Lizorkin and Besov spaces in the context of Laguerre expansions. Journal of Functional Analysis, 256(4), 1137–1188. https://doi.org/10.1016/j.jfa.2008.09.015
Kozono, H., & Yamazaki, M. (1994). Semilinear heat equations and the Navier-Stokes equation with distributions in the new function spaces as initial data. Comm. Partial Differential Equations, 19(5–6), 959–1014. https://doi.org/10.1007/978-4-431-68413-8_10
Liskevich, V., & Sobol, Z. (2003). Estimates of integral kernels for semigroups associated with second order elliptic operators with singular coefficients. Potential Analysis, 18, 359–390. https://doi.org/10.1023/A:1021877025938
Anna Mazzucato, L. (2003). Besov-Morrey spaces: Function space theory and applications to nonlinear PDE. Transactions of the American Mathematical Society, 355, 1297–1364. DOI: 10.2307/1194896
Anna Mazzucato, L. (2003). Decomposition of Besov-Morrey spaces. Proceedings of the Conference on Harmonic Analysis. Contemp. Math. 320, Amer. Math. Soc., Providence, RI, 279–294. DOI: 10.1090/conm/320/05613
Morrey, C. B. (1938). On the solutions of quasi-linear elliptic partial differential equations. Transactions of the American Mathematical Society, 43, 126–166. https://doi.org/10.2307/1989904
Milman, P. D. & Semenov, Y. A. (2004). Global heat kernel bounds via desingularizing weights. Journal of Functional Analysis, 212, 373–398. https://doi.org/10.1016/j.jfa.2003.12.008
Trong, N. N., Truong, L. X., Dung, T. T., & Vo, H. N. (2020). Triebel-Lizorkin-Morrey spaces associated with Hermite operators. Revista Matemática Complutense, 33, 527–555. https://doi.org/10.1007/s13163-019-00314-1