Singular integral operators on nilpotent Lie groups
نویسندگان
چکیده
منابع مشابه
Singular Spherical Maximal Operators on a Class of Step Two Nilpotent Lie Groups
Let H ∼= R ⋉ R be the Heisenberg group and let μt be the normalized surface measure for the sphere of radius t in R. Consider the maximal function defined by Mf = supt>0 |f ∗ μt|. We prove for n ≥ 2 that M defines an operator bounded on L(H) provided that p > 2n/(2n− 1). This improves an earlier result by Nevo and Thangavelu, and the range for L boundedness is optimal. We also extend the result...
متن کاملSingular Spherical Maximal Operators on a Class of Two Step Nilpotent Lie Groups
Let H be the Heisenberg group and let μt be the normalized surface measure for the sphere of radius t in R. Consider the maximal function defined by Mf = supt>0 |f ∗μt|. We prove for n ≥ 2 that M defines an operator bounded on L(H) provided that p > 2n/(2n − 1). This improves an earlier result by Nevo and Thangavelu, and the range for L boundedness is optimal. We also extend the result to a mor...
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To any connected and simply connected nilpotent Lie group N , one can associate its group of affine transformations Aff(N). In this paper, we study simply transitive actions of a given nilpotent Lie group G on another nilpotent Lie group N , via such affine transformations. We succeed in translating the existence question of such a simply transitive affine action to a corresponding question on ...
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ژورنال
عنوان ژورنال: Arkiv för Matematik
سال: 1980
ISSN: 0004-2080
DOI: 10.1007/bf02384677