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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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


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
  • © Copyright 1995 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 347 (1995), 2201-2212
  • MSC: Primary 47D06; Secondary 42B25, 43A85
  • DOI:
  • MathSciNet review: 1264824