Không gian Besov Morrey liên kết với toán tử Schrödinger với hàm thế bình phương nghịch đảo
Nội dung chính của bài viết
Tóm tắt
Cho là một toán tử Schrödinger với hàm thế bình phương nghịch đảo a|x|-2 trên R3 , n \geq 3. Mục tiêu chính của bài báo này là phát triển lý thuyết về các không gian Morrey–Besov mới gắn với toán tử L . Các kết quả này tổng quát hóa các kết quả tương ứng trong [T. A. Bui. Besov and Triebel-Lizorkin spaces for Schrödinger operators with inverse–square potentials and applications, J. Diff. Eq., 269 (2020), 641-688].
Từ khóa
Hàm thế bình phương nghịch đảo, không gian Morrey, không gian Besov.
Chi tiết bài viết
Tài liệu tham khảo
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