Geodesic
Endpoint Estimates of Riesz Transforms Associated with Generalized Schrödinger Operators
Canadian mathematical bulletin, Tome 61 (2018) no. 4, pp. 787-801

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

In this paper we establish the endpoint estimates and Hardy type estimates for the Riesz transform associated with the generalized Schrödinger operator.
DOI : 10.4153/CMB-2017-080-0
Mots-clés : 35J10, 42B20, 42B30, Schrödinger operator, fundamental solution, Riesz transform 
Liu, Yu; Qi, Shuai. Endpoint Estimates of Riesz Transforms Associated with Generalized Schrödinger Operators. Canadian mathematical bulletin, Tome 61 (2018) no. 4, pp. 787-801. doi: 10.4153/CMB-2017-080-0
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     title = {Endpoint {Estimates} of {Riesz} {Transforms} {Associated} with {Generalized} {Schr\"odinger} {Operators}},
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     doi = {10.4153/CMB-2017-080-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2017-080-0/}
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[1] [1] Auscher, P. and Ben Ali, B., Maximal inequalities and Riesz transform estimates on LP spaces for Schrb'dinger operators with nonnegative potentials. Ann. Inst. Fourier (Grenoble) 57 (2007), no. 6, 1975-2013. http://dx.doi.Org/10.58O2/aif.232O Google Scholar

[2] [2] Cao, J., Liu, Y., and Yang, Da., Hardy spaces associated to Schrodinger type operators . Houston J. Math. 36 (2010), no. 4,1067-1095. Google Scholar

[3] [3] Dziubanski, J. and Zienkiewicz, J., Hardy space H1 associated to Schrodinger operator with potential satisfying reverse Holder inequality. Rev. Mat. Iberoamericana 15 (1999), no. 2, 279-296. http://dx.doi.Org/10.4171/RMI/257 Google Scholar

[4] [4] Garcia-Cuerva, J. and de Francia, J. Rubio, Weighted norm inequalities and related topics. North-Holland Mathematics Studies, 116, Notas de Matemâtica, 104, North-Holland Publishing Co., Amsterdam, 1985. Google Scholar

[5] [5] Li, H.-Q., Estimations LP des opérateurs de Schrodinger sur les groupes nilpotents. J. Func. Anal. 161 (1999), no. 1, 152-218. http://dx.doi.Org/10.1006/jfan.1998.3347 Google Scholar

[6] [6] Lin, C., Liu, H., and Liu, Y., Hardy spaces associated with Schrodinger operators on the Heisenberg group. arxiv:1106.4960 Google Scholar

[7] [7] Liu, Y. and Dong, J., Some estimates of higher order Riesz transform related to Schrodinger operator. Potential. Anal. 32 (2010), no. 1, 41-55. http://dx.doi.Org/10.1007/s11118-009-9143-7 Google Scholar

[8] [8] Shen, Z., LP estimates for Schrb'dinger operators with certain potentials. Ann. Inst. Fourier (Grenoble) 45 (1995), 513–546. http://dx.doi.org/10.5802/aif.1463 Google Scholar

[9] [9] Shen, Z., On fundamental solutions of generalized Schrodinger operators. J. Funct. Anal. 167 (1999), 521–564. http://dx.doi.org/10.1006/jfan.1999.3455 Google Scholar

[10] [10] Taibleson, M. H. and Weiss, G., The molecular characterization of certain Hardy spaces. In: Representation theorems for Hardy spaces, Astérisque, 77, Soc. Math. France, Paris, 1980, pp. 67–149. Google Scholar

[11] [11] Wu, L. and Yan, L., Heat kernels, upper bounds and Hardy spaces associated to the generalized Schrodinger operators. J. Funct. Anal. 270 (2016), no. 10, 3709-3749. http://dx.doi.Org/10.1016/j.jfa.2O15.12.016 Google Scholar

[12] [12] Yang, Da., Yang, Do., and Zhou, Y., Endpoint properties of localized Riesz transforms and fractional integrals associated to Schrodinger operators. Potential Anal. 30 (2009), no. 3, 271-300. http://dx.doi.Org/10.1007/s11118-009-9116-x Google Scholar

[13] [13] Zhong, J., Harmonic analysis for some Schrodinger type operators. Ph.D., Princeton University, 1993. Google Scholar

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