Mathematics – Classical Analysis and ODEs
Scientific paper
2012-02-08
Mathematics
Classical Analysis and ODEs
31 pages
Scientific paper
In this paper we study Littlewood-Paley-Stein functions associated with the Poisson semigroup for the Hermite operator on functions with values in a UMD Banach space $\B.$ If we denote by $H$ the Hilbert space $L^2((0,\infty),dt/t),\gamma(H,\B)$ represents the space of $\gamma$-radonifying operators from $H$ into $\B.$ We prove that the Hermite square function defines bounded operators from $BMO_\mathcal{L}(\R,\B)$ (respectively, $H^1_\mathcal{L}(\R, \B)$) into $BMO_\mathcal{L}(\R,\gamma(H,\B))$ (respectively, $H^1_\mathcal{L}(\R, \gamma(H,\B))$), where $BMO_\mathcal{L}$ and $H^1_\mathcal{L}$ denote $BMO$ and Hardy spaces in the Hermite setting. Also, we obtain equivalent norms in $BMO_\mathcal{L}(\R, \B)$ and $H^1_\mathcal{L}(\R,\B)$ by using Littlewood-Paley-Stein functions. As a consequence of our results, we establish new characterizations of the UMD Banach spaces.
Betancor Jorge J.
Castro Alejandro J.
Curbelo Jezabel
Fariña Juan C.
Rodríguez-Mesa Lourdes
No associations
LandOfFree
$γ$-radonifying operators and UMD-valued Littlewood-Paley-Stein functions in the Hermite setting on BMO and Hardy spaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with $γ$-radonifying operators and UMD-valued Littlewood-Paley-Stein functions in the Hermite setting on BMO and Hardy spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and $γ$-radonifying operators and UMD-valued Littlewood-Paley-Stein functions in the Hermite setting on BMO and Hardy spaces will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-64544