Bất đẳng thức Hardy chứa toán tử Dunkl liên kết với HI-POTENTIAL
Nội dung chính của bài viết
Tóm tắt
Chúng tôi chứng minh bất đẳng thức dạng Hardy cho toán tử Dunkl liên kết với một HI-potential. Kết quả của chúng tôi là một sự mở rộng kết quả của Ghoussoub and Moradifam trong [11]
Từ khóa
HI-Potential, Hardy inequality, best constant.
Chi tiết bài viết
Tài liệu tham khảo
1. Adimurthi, Chaudhuri, N., & Ramaswamy, M. (2002). An improved Hardy-Sobolev inequality and its application. Proceedings of the American Mathematical Society, 130(2), 489–505.
2. Barbatis, G., Filippas, S., & Tertikas, A. (2003). Series expansion for Lp Hardy inequalities. Indiana University Mathematics Journal, 52(1), 171–190.
3. Barbatis, G., Filippas, S., & Tertikas, A. (2004). A unified approach to improved Lp Hardy inequalities with best constants. Transactions of the American Mathematical Society, 356(6), 2169–2196.
4. Bogdan, K., Dyda, B., & Kim, P. (2016). Hardy inequalities and non-explosion results for semigroups. Potential Analysis, 44, 229–247.
5. Cazacu, C., & Zuazua, E. (2013). Improved multipolar Hardy inequalities. In Studies in phase space analysis with applications to PDEs (pp. 35–52). Birkhäuser.
6. Davies, E. B. (1999). A review of Hardy inequalities. In The Maz'ya anniversary collection (Vol. 2, pp. 55–67). Birkhäuser.
7. Dolbeault, J., & Volzone, B. (2012). Improved Poincaré inequalities. Nonlinear Analysis, 75(16), 5985–6001.
8. Evans, W. D., & Lewis, R. T. (2007). Hardy and Rellich inequalities with remainders. Journal of Mathematical Inequalities, 1(4), 473–490.
9. Filippas, S., & Tertikas, A. (2002). Optimizing improved Hardy inequalities. Journal of Functional Analysis, 192(1), 186–233.
10. Ghoussoub, N., & Moradifam, A. (2011). Bessel pairs and optimal Hardy and Hardy-Rellich inequalities. Mathematische Annalen, 349(1), 1–57.
11. Ghoussoub, N., & Moradifam, A. (2013). Functional inequalities: New perspectives and new applications (Mathematical Surveys and Monographs, Vol. 187). Providence, RI: American Mathematical Society.
12. Kufner, A., Maligranda, L., & Persson, L.-E. (2007). The Hardy inequality: About its history and some related results. Vydavatelský Servis.
13. Kufner, A., & Persson, L.-E. (2003). Weighted inequalities of Hardy type. World Scientific.
14. Rösler, M. (2003). Dunkl operators: Theory and applications. In Orthogonal polynomials and special functions (pp. 93–135). Springer.
2. Barbatis, G., Filippas, S., & Tertikas, A. (2003). Series expansion for Lp Hardy inequalities. Indiana University Mathematics Journal, 52(1), 171–190.
3. Barbatis, G., Filippas, S., & Tertikas, A. (2004). A unified approach to improved Lp Hardy inequalities with best constants. Transactions of the American Mathematical Society, 356(6), 2169–2196.
4. Bogdan, K., Dyda, B., & Kim, P. (2016). Hardy inequalities and non-explosion results for semigroups. Potential Analysis, 44, 229–247.
5. Cazacu, C., & Zuazua, E. (2013). Improved multipolar Hardy inequalities. In Studies in phase space analysis with applications to PDEs (pp. 35–52). Birkhäuser.
6. Davies, E. B. (1999). A review of Hardy inequalities. In The Maz'ya anniversary collection (Vol. 2, pp. 55–67). Birkhäuser.
7. Dolbeault, J., & Volzone, B. (2012). Improved Poincaré inequalities. Nonlinear Analysis, 75(16), 5985–6001.
8. Evans, W. D., & Lewis, R. T. (2007). Hardy and Rellich inequalities with remainders. Journal of Mathematical Inequalities, 1(4), 473–490.
9. Filippas, S., & Tertikas, A. (2002). Optimizing improved Hardy inequalities. Journal of Functional Analysis, 192(1), 186–233.
10. Ghoussoub, N., & Moradifam, A. (2011). Bessel pairs and optimal Hardy and Hardy-Rellich inequalities. Mathematische Annalen, 349(1), 1–57.
11. Ghoussoub, N., & Moradifam, A. (2013). Functional inequalities: New perspectives and new applications (Mathematical Surveys and Monographs, Vol. 187). Providence, RI: American Mathematical Society.
12. Kufner, A., Maligranda, L., & Persson, L.-E. (2007). The Hardy inequality: About its history and some related results. Vydavatelský Servis.
13. Kufner, A., & Persson, L.-E. (2003). Weighted inequalities of Hardy type. World Scientific.
14. Rösler, M. (2003). Dunkl operators: Theory and applications. In Orthogonal polynomials and special functions (pp. 93–135). Springer.