We consider semigroups (Tt), which are contractive on LP(M) for all P ε [q, q'] and q ε[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 (Tt) may be unbounded on Li(M) and on Lq '(M). We prove that variants of the g-function are bounded on these Lebesgue spaces
Meda, S. (1995). On the Littlewood-Paley-Stein $g$-function. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 347(6), 2201-2212 [10.1090/S0002-9947-1995-1264824-6].
On the Littlewood-Paley-Stein $g$-function
Meda, S
1995
Abstract
We consider semigroups (Tt), which are contractive on LP(M) for all P ε [q, q'] and q ε[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 (Tt) may be unbounded on Li(M) and on Lq '(M). We prove that variants of the g-function are bounded on these Lebesgue spaces
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