TY - JOUR
T1 - On a maximal function on compact lie groups
AU - Cowling, Michael
AU - Meaney, Christopher
PY - 1989
Y1 - 1989
N2 - Suppose that G is a compact Lie group with finite centre. For each positive number j we consider the Ad(G)-invariant probability measure μscarried on the conjugacy class of exp(sHp) in G. This one-parameter family of measures is used to define a maximal function Mf, for each continuous function f on G. Our theorem states that there is an index p0in (1, 2), depending on G, such that the maximal operator J? is bounded on LP(G) when p is greater than p0. When the rank of G is greater than one, this provides an example of a controllable maximal operator coming from averages over a family of submanifolds, each of codimension greater than one.
AB - Suppose that G is a compact Lie group with finite centre. For each positive number j we consider the Ad(G)-invariant probability measure μscarried on the conjugacy class of exp(sHp) in G. This one-parameter family of measures is used to define a maximal function Mf, for each continuous function f on G. Our theorem states that there is an index p0in (1, 2), depending on G, such that the maximal operator J? is bounded on LP(G) when p is greater than p0. When the rank of G is greater than one, this provides an example of a controllable maximal operator coming from averages over a family of submanifolds, each of codimension greater than one.
UR - http://www.scopus.com/inward/record.url?scp=0038917081&partnerID=8YFLogxK
U2 - 10.1090/S0002-9947-1989-0958889-3
DO - 10.1090/S0002-9947-1989-0958889-3
M3 - Article
AN - SCOPUS:0038917081
VL - 315
SP - 811
EP - 822
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
SN - 0002-9947
IS - 2
ER -