On the Heisenberg group, the dyadic elliptic maximal operator is L^p bounded for all 2-by-2 matrices A except A = cI (one-parameter case) and A = diag(c, c*2^(2a)) (two-parameter case).
and W ainger, Stephen , Differentiation in lacunary directions , Proc
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Lacunary elliptic maximal operator on the Heisenberg group
On the Heisenberg group, the dyadic elliptic maximal operator is L^p bounded for all 2-by-2 matrices A except A = cI (one-parameter case) and A = diag(c, c*2^(2a)) (two-parameter case).