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 |
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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