Harmonic Analysis
Use of Hardy spaces and interpolation
Comptes Rendus. Mathématique, Volume 346 (2008) no. 13-14, pp. 745-748.

We want to describe an abstract construction of Hardy spaces H1 using an atomic decomposition and then we describe the use of these spaces in a point of view of interpolation. Mainly, we look for weakest assumptions to obtain an interpolation result between these Hardy spaces and Lebesgue spaces.

Nous présentons une construction abstraite d'espaces de Hardy H1 par une décomposition atomique et nous décrivons l'utilisation de ces espaces avec pour but de les interpoler. Nous donnerons alors des hypothèses les plus faibles pour obtenir un résultat d'interpolation entre ces « nouveaux » espaces de Hardy et les espaces de Lebesgue.

Published online:
DOI: 10.1016/j.crma.2008.05.009
Bernicot, Frédéric 1

1 Université Paris-Sud, Orsay et CNRS 8628, 91405 Orsay cedex, France
     author = {Bernicot, Fr\'ed\'eric},
     title = {Use of {Hardy} spaces and interpolation},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {745--748},
     publisher = {Elsevier},
     volume = {346},
     number = {13-14},
     year = {2008},
     doi = {10.1016/j.crma.2008.05.009},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2008.05.009/}
AU  - Bernicot, Frédéric
TI  - Use of Hardy spaces and interpolation
JO  - Comptes Rendus. Mathématique
PY  - 2008
SP  - 745
EP  - 748
VL  - 346
IS  - 13-14
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2008.05.009/
DO  - 10.1016/j.crma.2008.05.009
LA  - en
ID  - CRMATH_2008__346_13-14_745_0
ER  - 
%0 Journal Article
%A Bernicot, Frédéric
%T Use of Hardy spaces and interpolation
%J Comptes Rendus. Mathématique
%D 2008
%P 745-748
%V 346
%N 13-14
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2008.05.009/
%R 10.1016/j.crma.2008.05.009
%G en
%F CRMATH_2008__346_13-14_745_0
Bernicot, Frédéric. Use of Hardy spaces and interpolation. Comptes Rendus. Mathématique, Volume 346 (2008) no. 13-14, pp. 745-748. doi : 10.1016/j.crma.2008.05.009. http://www.numdam.org/articles/10.1016/j.crma.2008.05.009/

[1] Auscher, P.; Martell, J.M. Weighted norm inequalities, off-diagonal estimates and elliptic operators, Part I: General operator theory and weights, Adv. in Math., Volume 212 (2007), pp. 225-276

[2] F. Bernicot, Use of abstract Hardy spaces, Real interpolation and applications to bilinear operators (2008), submitted for publication

[3] F. Bernicot, J. Zhao, New Hardy spaces, arXiv:0712.3114 (2007), J. Funct. Anal., in press

[4] Bownik, M. Boundedness of operators on Hardy spaces via atomic decompositions, Proc. Amer. Math. Soc., Volume 133 (2007) no. 12, pp. 3535-3542

[5] Coifman, R.R.; Weiss, G. Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc., Volume 83 (1977) no. 4, pp. 569-645

[6] Duong, X.T.; Yan, L. New function spaces of BMO type, the John–Nirenberg inequality, interpolation and applications, Comm. Pures Appl. Math., Volume 58 (2005) no. 10, pp. 1375-1420

[7] García-Cuerva, J.; Rubio de Francia, J.L. Weighted Norm Inequalities and Related Topics, North-Holland Mathematics Studies, North-Holland, Amsterdam, 1985

[8] Martell, J.M. Sharp maximal functions associated with approximations of the identity in spaces of homogeneous type and applications, Studia Math., Volume 161 (2004), pp. 113-145

[9] Meda, S.; Sjögre, P.; Vallarino, M. On the H1-L1 boundedness of operators, Proc. Amer. Math. Soc. (2008)

[10] Meyer, Y.; Taibleson, M.; Weiss, G. Some functional analytic properties of the spaces Bq generated by blocks, Indiana Univ. Math. J., Volume 34 (1985), pp. 493-515

Cited by Sources: