A $T1$ criterion for Hermite-Calderón-Zygmund operators on the $BM{O}_H\left({ℝ}^n\right)$ 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.

In this paper we establish a $T1$ criterion for the boundedness of Hermite-Calderón -Zygmund operators on the $BM{O}_H\left({ℝ}^n\right)$ space naturally associated to the Hermite operator $H$. We apply this criterion in a systematic way to prove the boundedness on $BM{O}_H\left({ℝ}^n\right)$ of certain harmonic analysis operators related to $H$ (Riesz transforms, maximal operators, Littlewood-Paley $g$-functions and variation operators).

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

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