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


Author: Stefano Meda
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
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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.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1995-1264824-6
Keywords: $ g$-function, functional calculus, symmetric spaces
Article copyright: © Copyright 1995 American Mathematical Society

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