caa a22 4500 38630758X CHVBK 20180307111534.0 cr unu---uuuuu 161130e198808 xx s 000 0 eng 10.1017/S1446788700032328 doi S1446788700032328 pii (NATIONALLICENCE)cambridge-10.1017/S1446788700032328 Meaney Christopher Department of Mathematics Australian National University Canberra, ACT 2601, Australia Regularity of mean-values [Elektronische Daten] [Christopher Meaney] Let X be either the d-dimensional sphere or a compact, simply connected, simple, connected Lie group. We define a mean-value operator analogous to the spherical mean-value operator acting on integrable functions on Euclidean space. The value of this operator will be written as f (x, a), where x X and a varies over a torus A in the group of isometries of X. For each of these cases there is an interval pO < p ≦ 2, where the p0 depends on the geometry of X, such that if f is in Lp (X) then there is a set full measure in X and if x lies in this set, the function a f(x, a) has some Hölder continuity on compact subsets of the regular elements of A. Copyright © Australian Mathematical Society 1988 42 C 10 nationallicence 43 A 15 nationallicence Symmetric space nationallicence spherical function nationallicence Sobolev space nationallicence mean-value operator nationallicence maximal torus nationallicence Journal of the Australian Mathematical Society Cambridge University Press 45/1(1988-08), 117-126 1446-7887 45:1<117 1988 45 JAZ https://doi.org/10.1017/S1446788700032328 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S1446788700032328 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Meaney Christopher Department of Mathematics Australian National University Canberra, ACT 2601, Australia NATIONALLICENCE 773 0- Journal of the Australian Mathematical Society Cambridge University Press 45/1(1988-08), 117-126 1446-7887 45:1<117 1988 45 JAZ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge