A $T1$ criterion for Hermite-Calderón-Zygmund operators on the $BMO_{H}(\protect \mathbb{R}^{n})$ space and applications

Betancor, Jorge J.; Crescimbeni, Raquel; Fariña, Juan C.; Stinga, Pablo Raúl; Torrea, José L.

Geodesic

Parcourir par

T 1

criterion for Hermite-Calderón-Zygmund operators on the

B M O_{H} (ℝ^{n})

space and applications

Betancor, Jorge J. ; Crescimbeni, Raquel ; Fariña, Juan C. ; Stinga, Pablo Raúl ; Torrea, José L.

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 12 (2013) no. 1, pp. 157-187

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Résumé

In this paper we establish a $T 1$ criterion for the boundedness of Hermite-Calderón -Zygmund operators on the $B M O_{H} (ℝ^{n})$ space naturally associated to the Hermite operator $H$ . We apply this criterion in a systematic way to prove the boundedness on $B M O_{H} (ℝ^{n})$ of certain harmonic analysis operators related to $H$ (Riesz transforms, maximal operators, Littlewood-Paley $g$ -functions and variation operators).

Publié le : 2019-02-21

MR Zbl

Classification : 42B20, 42B25, 42B35, 35J10, 42B15, 42C10

@article{ASNSP_2013_5_12_1_157_0,
     author = {Betancor, Jorge J. and Crescimbeni, Raquel and Fari\~na, Juan C. and Stinga, Pablo Ra\'ul and Torrea, Jos\'e L.},
     title = {A $T1$ criterion for {Hermite-Calder\'on-Zygmund} operators on the $BMO_{H}(\protect \mathbb{R}^{n})$ space and applications},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {157--187},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 12},
     number = {1},
     year = {2013},
     mrnumber = {3088440},
     zbl = {1276.42014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ASNSP_2013_5_12_1_157_0/}
}

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AU  - Betancor, Jorge J.
AU  - Crescimbeni, Raquel
AU  - Fariña, Juan C.
AU  - Stinga, Pablo Raúl
AU  - Torrea, José L.
TI  - A $T1$ criterion for Hermite-Calderón-Zygmund operators on the $BMO_{H}(\protect \mathbb{R}^{n})$ space and applications
JO  - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY  - 2013
SP  - 157
EP  - 187
VL  - 12
IS  - 1
PB  - Scuola Normale Superiore, Pisa
UR  - http://geodesic.mathdoc.fr/item/ASNSP_2013_5_12_1_157_0/
LA  - en
ID  - ASNSP_2013_5_12_1_157_0
ER  -

%0 Journal Article
%A Betancor, Jorge J.
%A Crescimbeni, Raquel
%A Fariña, Juan C.
%A Stinga, Pablo Raúl
%A Torrea, José L.
%T A $T1$ criterion for Hermite-Calderón-Zygmund operators on the $BMO_{H}(\protect \mathbb{R}^{n})$ space and applications
%J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
%D 2013
%P 157-187
%V 12
%N 1
%I Scuola Normale Superiore, Pisa
%U http://geodesic.mathdoc.fr/item/ASNSP_2013_5_12_1_157_0/
%G en
%F ASNSP_2013_5_12_1_157_0

Betancor, Jorge J.; Crescimbeni, Raquel; Fariña, Juan C.; Stinga, Pablo Raúl; Torrea, José L. A $T1$ criterion for Hermite-Calderón-Zygmund operators on the $BMO_{H}(\protect \mathbb{R}^{n})$ space and applications. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 12 (2013) no. 1, pp. 157-187. http://geodesic.mathdoc.fr/item/ASNSP_2013_5_12_1_157_0/