A maximal function on the discrete Heisenberg group with applications to ergodic theory

2006 ◽  
pp. 123-130
Author(s):  
Stephen Wainger
Keyword(s):  
Heisenberg Group ◽  
Ergodic Theory ◽  
Maximal Function ◽  
Discrete Heisenberg Group

scholarly journals On the lacunary spherical maximal function on the Heisenberg group

2021 ◽  
Vol 280 (3) ◽  
pp. 108832
Author(s):  
Pritam Ganguly ◽  
Sundaram Thangavelu
Keyword(s):  
Heisenberg Group ◽  
Maximal Function

scholarly journals A Wiener Lemma for the discrete Heisenberg group

2016 ◽  
Vol 180 (3) ◽  
pp. 485-525
Author(s):  
Martin Göll ◽  
Klaus Schmidt ◽  
Evgeny Verbitskiy
Keyword(s):  
Heisenberg Group ◽  
Discrete Heisenberg Group

scholarly journals AFFINE ACTIONS ON NON-ARCHIMEDEAN TREES

2013 ◽  
Vol 23 (02) ◽  
pp. 217-253 ◽  
Author(s):  
SHANE O. ROURKE
Keyword(s):  
Abelian Group ◽  
Heisenberg Group ◽  
Isometric Action ◽  
Length Functions ◽  
Common Generalization ◽  
New Class ◽  
Discrete Heisenberg Group ◽  
Affine Action ◽  
Affine Actions

We initiate the study of affine actions of groups on Λ-trees for a general ordered abelian group Λ; these are actions by dilations rather than isometries. This gives a common generalization of isometric action on a Λ-tree, and affine action on an ℝ-tree as studied by Liousse. The duality between based length functions and actions on Λ-trees is generalized to this setting. We are led to consider a new class of groups: those that admit a free affine action on a Λ-tree for some Λ. Examples of such groups are presented, including soluble Baumslag–Solitar groups and the discrete Heisenberg group.

scholarly journals The Equivalence of Operator Norm between the Hardy-Littlewood Maximal Function and Truncated Maximal Function on the Heisenberg Group

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Xiang Li ◽  
Xingsong Zhang
Keyword(s):  
Heisenberg Group ◽  
Maximal Function ◽  
Operator Norm ◽  
Littlewood Maximal Function ◽  
Weak Norm

In this article, we define a kind of truncated maximal function on the Heisenberg space by M γ c f x = sup 0 < r < γ 1 / m B x , r ∫ B x , r f y d y . The equivalence of operator norm between the Hardy-Littlewood maximal function and the truncated maximal function on the Heisenberg group is obtained. More specifically, when 1 < p < ∞ , the L p norm and central Morrey norm of truncated maximal function are equal to those of the Hardy-Littlewood maximal function. When p = 1 , we get the equivalence of weak norm L 1 ⟶ L 1 , ∞ and M ̇ 1 , λ ⟶ W ̇ M 1 , λ . Those results are generalization of previous work on Euclid spaces.

Strong Morita Equivalence for Heisenberg C*-Algebras and the Positive Cones of Their K 0-Groups

1988 ◽  
Vol 40 (04) ◽  
pp. 833-864 ◽  
Author(s):  
Judith A. Packer
Keyword(s):  
Heisenberg Group ◽  
Morita Equivalence ◽  
Equivalence Classes ◽  
Crossed Products ◽  
C Algebras ◽  
Projective Representations ◽  
Discrete Heisenberg Group ◽  
Strong Morita Equivalence

In [14] we began a study of C*-algebras corresponding to projective representations of the discrete Heisenberg group, and classified these C*-algebras up to *-isomorphism. In this sequel to [14] we continue the study of these so-called Heisenberg C*-algebras, first concentrating our study on the strong Morita equivalence classes of these C*-algebras. We recall from [14] that a Heisenberg C*-algebra is said to be of class i, i ∊ {1, 2, 3}, if the range of any normalized trace on its K 0 group has rank i as a subgroup of R; results of Curto, Muhly, and Williams [7] on strong Morita equivalence for crossed products along with the methods of [21] and [14] enable us to construct certain strong Morita equivalence bimodules for Heisenberg C*-algebras.

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