Abstract
We consider Banach valued Hardy and BMO spaces in the Bessel setting. Square functions associated with Poisson semigroups for Bessel operators are defined by using fractional derivatives. If (Formula presented.) is a UMD Banach space we obtain for (Formula presented.)-valued Hardy and BMO spaces equivalent norms involving γ-radonifying operators and square functions. We also establish characterizations of UMD Banach spaces by means of Hardy and BMO-boundedness properties of g-functions associated to Bessel–Poisson semigroup.
| Original language | English |
|---|---|
| Pages (from-to) | 319-374 |
| Number of pages | 56 |
| Journal | Integral Equations and Operator Theory |
| Volume | 81 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2015 |
Keywords
- BMO
- Bessel operators
- Hardy
- Square functions
- UMD spaces
ASJC Scopus subject areas
- Analysis
- Algebra and Number Theory
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Betancor, J. J., Castro, A. J., & Rodríguez-Mesa, L. (2015). UMD-valued square functions associated with Bessel operators in Hardy and BMO spaces. Integral Equations and Operator Theory, 81(3), 319-374. https://doi.org/10.1007/s00020-014-2202-5