In this paper, we develop an abstract framework for John-Nirenberg inequalities associated to BMO-type spaces. This work can be seen as the sequel of [6], where the authors introduced a very general framework for atomic and molecular Hardy spaces. Moreover, we show that our assumptions allow us to recover some already known John-Nirenberg inequalities. We give applications to the atomic Hardy spaces too.
@article{ASNSP_2012_5_11_3_475_0, author = {Bernico, Fr\'ed\'eric and Zhao, Jiman}, title = {Abstract framework for {John-Nirenberg} inequalities and applications to {Hardy} spaces}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {475--501}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 11}, number = {3}, year = {2012}, mrnumber = {3059835}, zbl = {1266.42029}, language = {en}, url = {http://archive.numdam.org/item/ASNSP_2012_5_11_3_475_0/} }
TY - JOUR AU - Bernico, Frédéric AU - Zhao, Jiman TI - Abstract framework for John-Nirenberg inequalities and applications to Hardy spaces JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2012 SP - 475 EP - 501 VL - 11 IS - 3 PB - Scuola Normale Superiore, Pisa UR - http://archive.numdam.org/item/ASNSP_2012_5_11_3_475_0/ LA - en ID - ASNSP_2012_5_11_3_475_0 ER -
%0 Journal Article %A Bernico, Frédéric %A Zhao, Jiman %T Abstract framework for John-Nirenberg inequalities and applications to Hardy spaces %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2012 %P 475-501 %V 11 %N 3 %I Scuola Normale Superiore, Pisa %U http://archive.numdam.org/item/ASNSP_2012_5_11_3_475_0/ %G en %F ASNSP_2012_5_11_3_475_0
Bernico, Frédéric; Zhao, Jiman. Abstract framework for John-Nirenberg inequalities and applications to Hardy spaces. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 11 (2012) no. 3, pp. 475-501. http://archive.numdam.org/item/ASNSP_2012_5_11_3_475_0/
[1] P. Auscher, On necessary and sufficient conditions for estimates of Riesz transforms associated to elliptic operators on and related estimates, Mem. Amer. Math. Soc. 186 no.871 (2007). | MR | Zbl
[2] N. Badr and F. Bernicot, Abstract Hardy-Sobolev spaces and Interpolation, J. Funct. Anal. 259 (2010), 1169–1208. | MR | Zbl
[3] F. Bernicot, Use of abstract Hardy spaces, real interpolation and applications to bilinear operators, Math. Z. 265 (2010), 365–400. | MR | Zbl
[4] F. Bernicot, A T(1)-Theorem in relation to a semigroup of operators and applications to new paraproducts, Trans. Amer. Math. Soc. (2012), to appear. | MR | Zbl
[5] F. Bernicot and J. M. Martell, Self-improving properties for abstract Poincaré type inequalities, arxiv:1107.2260. | MR
[6] F. Bernicot and J. Zhao, New Abstract Hardy Spaces, J. Funct. Anal. 255 (2008), 1761–1796. | MR | Zbl
[7] R. Coifman and G. Weiss, Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc. 83 (1977), 569–645. | MR | Zbl
[8] D. Deng, X. T. Duong and L. Yan, A characterization of the Morrey-Campanato spaces, Math. Z. 250 (2005), 640–655. | MR | Zbl
[9] X.T. Duong and L. Yan, Duality of Hardy and BMO spaces associated with operators with heat kernel bounds, J. Amer. Math. Soc. 18 (2005), 943–973. | MR | Zbl
[10] X. T. Duong and L. Yan, New function spaces of BMO type, the John-Niremberg inequality, Interplation and Applications, Comm. Pures Appl. Math. 58 (2005), 1375–1420. | MR | Zbl
[11] J. Dziubański and M. Preisner, Remarks on spectral multiplier theorems on Hardy spaces associated with semigroups of operators, Rev. Un. Mat. Argentina 50 (2009), 201–215. | MR | Zbl
[12] C. Fefferman, Characterizations of bounded mean oscillation, Bull. Amer. Math. Soc. 77 (1971), 587–588. | MR | Zbl
[13] C. Fefferman and E. M. Stein, spaces of several variables, Acta Math. 129 (1971), 137–193. | MR | Zbl
[14] S. Hofmann and S. Mayboroda, Hardy and BMO spaces associated to divergence form elliptic operators, Math. Ann. 344 (2009), 37–116. | MR | Zbl
[15] A. Jiménez-del-Toro and J. M. Martell, Self-improvement of Poincaré type inequalities associated with approximations of the identity and semigroups, submitted (2010). | MR | Zbl
[16] A. Jiménez-del-Toro, Exponential self-improvement of generalized Poincaré inequalities associated with approximations of the identity and semigroups, Trans. Amer. Math. Soc. 364 (2012), 637–660. | MR | Zbl
[17] F. John and L. Nirenberg, On functions of bounded mean oscillation, Comm. Pure Appl. Math. 14 (1961), 785–799. | MR | Zbl
[18] W. Li, John-Nirenberg type inequalities for the Morrey-Campanato spaces, J. Inequal Appl. 2008 (2008). | EuDML | MR | Zbl
[19] E. M. Stein, “Harmonic Analysis: Real Variable Methods, Orthogonality, and Oscillatory Integrals”, Princeton Univ. Press, 1993. | MR | Zbl