Remark on commutative approximate identities on homogeneous groups

Remark on commutative approximate identities on homogeneous groups
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by Jacek Dziubański PDF

Proc. Amer. Math. Soc. 114 (1992), 1015-1016 Request permission

We give, using the functional calculus of Hulanicki [4], a construction of a commutative approximate identity on every homogeneous group.

References

Jacek Dziubański, A remark on a Marcinkiewicz-Hörmander multiplier theorem for some nondifferential convolution operators, Colloq. Math. 58 (1989), no. 1, 77–83. MR 1028162, DOI 10.4064/cm-58-1-77-83
G. B. Folland and Elias M. Stein, Hardy spaces on homogeneous groups, Mathematical Notes, vol. 28, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1982. MR 657581
PawełGłowacki, Stable semigroups of measures as commutative approximate identities on nongraded homogeneous groups, Invent. Math. 83 (1986), no. 3, 557–582. MR 827368, DOI 10.1007/BF01394423
Andrzej Hulanicki, A functional calculus for Rockland operators on nilpotent Lie groups, Studia Math. 78 (1984), no. 3, 253–266. MR 782662, DOI 10.4064/sm-78-3-253-266