Abstract
In this paper, we characterize the Lebesgue Bochner spaces (Formula presented.), by using Littlewood–Paley g-functions in the Hermite setting, provided that B is a UMD Banach space. We use (Formula presented.)-radonifying operators (Formula presented.) where (Formula presented.). We also characterize the UMD Banach spaces in terms of (Formula presented.) boundedness of Hermite Littlewood–Paley g-functions.
| Original language | English |
|---|---|
| Pages (from-to) | 1397-1430 |
| Number of pages | 34 |
| Journal | Annali di Matematica Pura ed Applicata |
| Volume | 193 |
| Issue number | 5 |
| DOIs | |
| Publication status | Published - Jan 1 2014 |
Keywords
- (Formula presented.)-radonifying operators
- Hermite operator
- Littlewood–Paley g-functions
- UMD Banach spaces
ASJC Scopus subject areas
- Applied Mathematics
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Cite this
Betancor, J. J., Castro, A. J., Curbelo, J., Fariña, J. C., & Rodríguez-Mesa, L. (2014). Square functions in the Hermite setting for functions with values in UMD spaces. Annali di Matematica Pura ed Applicata, 193(5), 1397-1430. https://doi.org/10.1007/s10231-013-0335-9