The Lusin Theorem and Horizontal Graphs in the Heisenberg Group
In this paper we prove that every collection of measurable functions fα , |α| = m, coincides a.e. withmth order derivatives of a function g ∈ Cm−1 whose derivatives of order m − 1 may have any modulus of continuity weaker than that of a Lipschitz function. This is a stronger version of earlier resul...
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De Gruyter
2013-11-01
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| Series: | Analysis and Geometry in Metric Spaces |
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| Online Access: | https://doi.org/10.2478/agms-2013-0008 |
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doaj-026d141eb1de41e78ece34481e99dcba2021-09-06T19:41:04ZengDe GruyterAnalysis and Geometry in Metric Spaces2299-32742013-11-011201329530110.2478/agms-2013-0008agms-2013-0008The Lusin Theorem and Horizontal Graphs in the Heisenberg GroupHajłasz Piotr0Mirra Jacob1Department of Mathematics, University of Pittsburgh, 301 Thackeray Hall, Pittsburgh, PA 15260, USADepartment of Mathematics, University of Pittsburgh, 301 Thackeray Hall, Pittsburgh, PA 15260, USAIn this paper we prove that every collection of measurable functions fα , |α| = m, coincides a.e. withmth order derivatives of a function g ∈ Cm−1 whose derivatives of order m − 1 may have any modulus of continuity weaker than that of a Lipschitz function. This is a stronger version of earlier results of Lusin, Moonens-Pfeffer and Francos. As an application we construct surfaces in the Heisenberg group with tangent spaces being horizontal a.e.https://doi.org/10.2478/agms-2013-0008lusin theorem heisenberg group characteristic points 46e3546e30 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Hajłasz Piotr Mirra Jacob |
| spellingShingle |
Hajłasz Piotr Mirra Jacob The Lusin Theorem and Horizontal Graphs in the Heisenberg Group Analysis and Geometry in Metric Spaces lusin theorem heisenberg group characteristic points 46e35 46e30 |
| author_facet |
Hajłasz Piotr Mirra Jacob |
| author_sort |
Hajłasz Piotr |
| title |
The Lusin Theorem and Horizontal Graphs in the
Heisenberg Group |
| title_short |
The Lusin Theorem and Horizontal Graphs in the
Heisenberg Group |
| title_full |
The Lusin Theorem and Horizontal Graphs in the
Heisenberg Group |
| title_fullStr |
The Lusin Theorem and Horizontal Graphs in the
Heisenberg Group |
| title_full_unstemmed |
The Lusin Theorem and Horizontal Graphs in the
Heisenberg Group |
| title_sort |
lusin theorem and horizontal graphs in the
heisenberg group |
| publisher |
De Gruyter |
| series |
Analysis and Geometry in Metric Spaces |
| issn |
2299-3274 |
| publishDate |
2013-11-01 |
| description |
In this paper we prove that every collection of measurable
functions fα , |α| = m, coincides a.e. withmth order derivatives
of a function g ∈ Cm−1 whose derivatives of order m − 1 may
have any modulus of continuity weaker than that of a Lipschitz
function. This is a stronger version of earlier results of Lusin,
Moonens-Pfeffer and Francos. As an application we construct
surfaces in the Heisenberg group with tangent spaces being
horizontal a.e. |
| topic |
lusin theorem heisenberg group characteristic points 46e35 46e30 |
| url |
https://doi.org/10.2478/agms-2013-0008 |
| work_keys_str_mv |
AT hajłaszpiotr thelusintheoremandhorizontalgraphsintheheisenberggroup AT mirrajacob thelusintheoremandhorizontalgraphsintheheisenberggroup AT hajłaszpiotr lusintheoremandhorizontalgraphsintheheisenberggroup AT mirrajacob lusintheoremandhorizontalgraphsintheheisenberggroup |
| _version_ |
1717767169725431808 |