P. Auscher, E. Russ, and P. Tchamitchian, Hardy Sobolev spaces on strongly Lipschitz domains of <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msup></mml:math>, Journal of Functional Analysis, vol.218, issue.1, pp.54-109, 2005.
DOI : 10.1016/j.jfa.2004.06.005

F. Bernicot, A $T(1)$-theorem in relation to a semigroup of operators and applications to new paraproducts, Transactions of the American Mathematical Society, vol.364, issue.11, pp.6071-6108, 2012.
DOI : 10.1090/S0002-9947-2012-05609-1

URL : https://hal.archives-ouvertes.fr/hal-00487080

J. J. Betancor, R. Crescimbeni, J. C. Farina, P. R. Stinga, and J. L. Torrea, A T 1 criterion for Hermite-Calderón-Zygmund operators on the BM O H (R n ) space and applications, Ann. Sc. Norm. Super. Pisa Cl. Sci, issue.5 1, pp.12-157, 2013.

A. Bonami, S. Grellier, and L. D. Ky, Paraproducts and products of functions in <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mi mathvariant="italic">BMO</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msup><mml:mi mathvariant="double-struck">R</mml:mi><mml:mi>n</mml:mi></mml:msup><mml:mo stretchy="false">)</mml:mo></mml:math> and <mml:math altimg="si2.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:msup><mml:mi mathvariant="script">H</mml:mi><mml:mn>1</mml:mn></mml:msup><mml:mo stretchy="false">(</mml:mo><mml:msup><mml:mi mathvariant="double-struck">R</mml:mi><mml:mi>n</mml:mi></mml:msup><mml:mo stretchy="false">)</mml:mo></mml:math> through wavelets, Journal de Math??matiques Pures et Appliqu??es, vol.97, issue.3, pp.230-241, 2012.
DOI : 10.1016/j.matpur.2011.06.002

B. Bongioanni, E. Harboure, and O. Salinas, Riesz transforms related to Schr??dinger operators acting on BMO type spaces, Journal of Mathematical Analysis and Applications, vol.357, issue.1, pp.115-131, 2009.
DOI : 10.1016/j.jmaa.2009.03.048

B. Bongioanni, E. Harboure, and O. Salinas, Commutators of Riesz Transforms Related to??Schr??dinger Operators, Journal of Fourier Analysis and Applications, vol.45, issue.2, pp.115-134, 2011.
DOI : 10.1007/s00041-010-9133-6

M. Bownik, Boundedness of operators on Hardy spaces via atomic decompositions, Proc. Amer, pp.3535-3542, 2005.

M. Bramanti and L. Brandolini, Estimates of BM O type for singular integrals on spaces of homogeneous type and applications to hypoelliptic PDEs, Rev. Mat. Iberoamericana, vol.21, issue.2, pp.511-556, 2005.

T. A. Bui, Weighted estimates for commutators of some singular integrals related to Schr??dinger operators, Bulletin des Sciences Math??matiques, vol.138, issue.2, pp.270-292, 2014.
DOI : 10.1016/j.bulsci.2013.06.007

D. Chang, G. Dafni, and E. M. Stein, Hardy spaces, BM O, and boundary value problems for the Laplacian on a smooth domain in R n, Transactions of the American Mathematical Society, vol.351, issue.04, pp.1605-1661, 1999.
DOI : 10.1090/S0002-9947-99-02111-X

R. R. Coifman, R. Rochberg, and G. Weiss, Factorization Theorems for Hardy Spaces in Several Variables, The Annals of Mathematics, vol.103, issue.3, pp.611-635, 1976.
DOI : 10.2307/1970954

G. Dafni, Hardy spaces on strongly pseudoconvex domains in C n and domains of finite type in C 2, 1993.

G. David and J. Journé, A Boundedness Criterion for Generalized Calderon-Zygmund Operators, The Annals of Mathematics, vol.120, issue.2, pp.371-397, 1984.
DOI : 10.2307/2006946

J. Dziuba´nskidziuba´nski, G. Garrigós, T. Martínez, J. Torrea, and J. Zienkiewicz, BMO spaces related to Schr??dinger operators with potentials satisfying a reverse H??lder inequality, Mathematische Zeitschrift, vol.45, issue.2, pp.329-356, 2005.
DOI : 10.1007/s00209-004-0701-9

J. Dziuba´nskidziuba´nski and J. Zienkiewicz, Hardy space H 1 associated to Schrödinger operator with potential satisfying reverse Hölder inequality, Rev. Mat. Iberoamericana, vol.15, pp.279-296, 1999.

C. Fefferman and E. M. Stein, Hp spaces of several variables, Acta Mathematica, vol.129, issue.0, pp.137-193, 1972.
DOI : 10.1007/BF02392215

M. Frazier and B. Jawerth, A discrete transform and decompositions of distribution spaces, Journal of Functional Analysis, vol.93, issue.1, pp.93-127, 1990.
DOI : 10.1016/0022-1236(90)90137-A

F. W. Gehring, The Lp-integrability of the partial derivatives of A quasiconformal mapping, Acta Mathematica, vol.130, issue.0, pp.265-277, 1973.
DOI : 10.1007/BF02392268

D. Goldberg, A local version of real Hardy spaces, Duke Mathematical Journal, vol.46, issue.1, pp.27-42, 1979.
DOI : 10.1215/S0012-7094-79-04603-9

Z. Guo, P. Li, and L. Peng, <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:msup><mml:mi>L</mml:mi><mml:mi>p</mml:mi></mml:msup></mml:math> boundedness of commutators of Riesz transforms associated to Schr??dinger operator, Journal of Mathematical Analysis and Applications, vol.341, issue.1, pp.421-432, 2008.
DOI : 10.1016/j.jmaa.2007.05.024

S. Hofmann, G. Lu, D. Mitrea, M. Mitrea, and L. Yan, Hardy spaces associated to nonnegative self-adjoint operators satisfying Davies-Gaffney estimates, Memoirs of the AMS, vol.214, issue.1007, 2011.
DOI : 10.1090/s0065-9266-2011-00624-6

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.219.3246

S. Hofmann, S. Mayboroda, and A. Mcintosh, Second order elliptic operators with complex bounded measurable coeffcients in L p , Sobolev and Hardy spaces, Ann. Sci. ´ Ec

S. Janson, On functions with conditions on the mean oscillation, Arkiv f??r Matematik, vol.14, issue.1-2, pp.189-196, 1976.
DOI : 10.1007/BF02385834

S. Janson, J. Peetre, and S. Semmes, On the action of Hankel and Toeplitz operators on some function spaces. Duke Math, J, vol.51, issue.4, pp.937-958, 1984.

P. Koskela, D. Yang, and Y. Zhou, A characterization of Haj??asz???Sobolev and Triebel???Lizorkin spaces via grand Littlewood???Paley functions, Journal of Functional Analysis, vol.258, issue.8, pp.2637-2661, 2010.
DOI : 10.1016/j.jfa.2009.11.004

L. D. Ky, New Hardy Spaces of Musielak???Orlicz Type and Boundedness of Sublinear Operators, Integral Equations and Operator Theory, vol.29, issue.8, pp.115-150, 2014.
DOI : 10.1007/s00020-013-2111-z

URL : https://hal.archives-ouvertes.fr/hal-00578059

L. D. Ky, Bilinear decompositions and commutators of singular integral operators, Transactions of the American Mathematical Society, vol.365, issue.6, pp.2931-2958, 2013.
DOI : 10.1090/S0002-9947-2012-05727-8

URL : https://hal.archives-ouvertes.fr/hal-00589824

L. D. Ky, On weak * -convergence in H 1 L (R d ). Potential Anal, pp.355-368, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00696432

H. Li, EstimationsLpdes op??rateurs de Schr??dinger sur les groupes nilpotents, Journal of Functional Analysis, vol.161, issue.1, pp.152-218, 1999.
DOI : 10.1006/jfan.1998.3347

URL : http://doi.org/10.1006/jfan.1998.3347

P. Li and L. Peng, The decomposition of product space H 1 L × BM O L, J. Math. Anal

P. Li and L. Peng, ENDPOINT ESTIMATES FOR COMMUTATORS OF RIESZ TRANSFORMS ASSOCIATED WITH SCHR??DINGER OPERATORS, Bulletin of the Australian Mathematical Society, vol.45, issue.03, pp.367-389, 2010.
DOI : 10.1006/jfan.1998.3347

T. Ma, P. R. Stinga, J. L. Torrea, and C. Zhang, Regularity estimates in H??lder spaces for Schr??dinger operators via a $$T1$$ theorem, Annali di Matematica Pura ed Applicata, vol.198, issue.62, pp.561-589, 2014.
DOI : 10.1007/s10231-012-0291-9

E. Nakai, A generalization of Hardy spaces H p by using atoms, Acta Mathematica Sinica, English Series, vol.34, issue.3, pp.1243-1268, 2008.
DOI : 10.1007/s10114-008-7626-x

M. Paluszy´nskipaluszy´nski, Characterization of Lipschitz spaces via the commutator operator of Coifman, Rochberg and Weiss: A multiplier theorem for the semigroup of contractions. Thesis (Ph.D.)-Washington University in St, 1992.

M. Papadimitrakis and J. A. Virtanen, Hankel and Toeplitz Transforms on H 1: Continuity, Compactness and Fredholm Properties, Integral Equations and Operator Theory, vol.61, issue.4, pp.573-591, 2008.
DOI : 10.1007/s00020-008-1609-2

URL : http://centaur.reading.ac.uk/29128/1/HankelOnH1_REF.pdf

C. Pérez, Endpoint Estimates for Commutators of Singular Integral Operators, Journal of Functional Analysis, vol.128, issue.1, pp.163-185, 1995.
DOI : 10.1006/jfan.1995.1027

C. Pérez and G. Pradolini, Sharp weighted endpoint estimates for commutators of singular integrals. Michigan Math, J, vol.49, issue.1, pp.23-37, 2001.

Z. Shen, $L^p$ estimates for Schr??dinger operators with certain potentials, Annales de l???institut Fourier, vol.45, issue.2, pp.513-546, 1995.
DOI : 10.5802/aif.1463

L. Song and L. Yan, Riesz transforms associated to Schr??dinger operators on weighted Hardy spaces, Journal of Functional Analysis, vol.259, issue.6, pp.1466-1490, 2010.
DOI : 10.1016/j.jfa.2010.05.015

URL : http://doi.org/10.1016/j.jfa.2010.05.015

D. A. Stegenga, Bounded Toeplitz Operators on H 1 and Applications of the Duality Between H 1 and the Functions of Bounded Mean Oscillation, American Journal of Mathematics, vol.98, issue.3, pp.573-589, 1976.
DOI : 10.2307/2373807

Y. Sun and W. Su, Interior <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:msup><mml:mi>h</mml:mi><mml:mn>1</mml:mn></mml:msup></mml:math>-estimates for second order elliptic equations with vanishing LMO coefficients, Journal of Functional Analysis, vol.234, issue.2, pp.235-260, 2006.
DOI : 10.1016/j.jfa.2005.10.004

L. Tang, Weighted norm inequalities for commutators of Littlewood-Paley functions related to Schrödinger operators

C. Tang and C. Bi, The boundedness of commutator of Riesz transform associated with Schr??dinger operators on a Hardy space, Journal of Function Spaces and Applications, vol.7, issue.3, pp.241-250, 2009.
DOI : 10.1155/2009/203934

D. Yang and D. Yang, Characterizations of localized BMO(??? n ) via commutators of localized Riesz transforms and fractional integrals associated to Schr??dinger operators, Collectanea mathematica, vol.30, issue.1, pp.65-79, 2010.
DOI : 10.1007/BF03191227

D. Yang and S. Yang, Local Hardy spaces of Musielak-Orlicz type and their applications, Science China Mathematics, vol.29, issue.8, pp.1677-1720, 2012.
DOI : 10.1007/s11425-012-4377-z

D. Yang and Y. Zhou, Localized Hardy spaces $H^{1}$ related to admissible functions on RD-spaces and applications to Schr??dinger operators, Transactions of the American Mathematical Society, vol.363, issue.03, pp.1197-1239, 2011.
DOI : 10.1090/S0002-9947-2010-05201-8

J. Zhong, Harmonic analysis for some Schrödinger type operators. Thesis (Ph.D.)- Princeton University, 1993.