Abstract
In this paper we consider conical square functions in the Bessel, Laguerre and Schrödinger settings where the functions take values in UMD Banach spaces. Following a recent paper of Hytönen, van Neerven and Portal [36], in order to define our conical square functions, we use γ-radonifying operators. We obtain new equivalent norms in the Lebesgue–Bochner spaces Lp((0,∞),B) and Lp(Rn,B), 1<p<∞, in terms of our square functions, provided that B is a UMD Banach space. Our results can be seen as Banach valued versions of known scalar results for square functions.
| Original language | English |
|---|---|
| Pages (from-to) | 32-75 |
| Number of pages | 44 |
| Journal | Journal of Mathematical Analysis and Applications |
| Volume | 447 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - Mar 1 2017 |
Keywords
- Bessel
- Conical square functions
- Laguerre
- Schrödinger
- UMD Banach spaces
- Vector-valued harmonic analysis
ASJC Scopus subject areas
- Analysis
- Applied Mathematics
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Castro, A. J., Betancor, J. J., Fariña, J. C., & Rodríguez-Mesa, L. (2017). Conical square functions associated with Bessel, Laguerre and Schrödinger operators in UMD Banach spaces. Journal of Mathematical Analysis and Applications, 447(1), 32-75. https://doi.org/10.1016/j.jmaa.2016.10.006