## On the Littlewood-Paley-Stein $g$-function

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- by Stefano Meda PDF
- Trans. Amer. Math. Soc.
**347**(1995), 2201-2212 Request permission

## Abstract:

We consider semigroups $({T_t})$, which are contractive on ${L^p}(M)$ for all $p \in [q,q’]$ and $q \in [1,2)$. We give an example (on symmetric spaces of the noncompact type) which shows that the Littlewood-Paley-Stein $g$-function associated to the infinitesimal generator of $({T_t})$ may be unbounded on ${L^q}(M)$ and on ${L^{q’}}(M)$. We prove that variants of the $g$-function are bounded on these Lebesgue spaces.## References

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## Additional Information

- © Copyright 1995 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**347**(1995), 2201-2212 - MSC: Primary 47D06; Secondary 42B25, 43A85
- DOI: https://doi.org/10.1090/S0002-9947-1995-1264824-6
- MathSciNet review: 1264824