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A left inverse approach to sharp Sobolev inequalities

Hindov, Raul LU orcid (2025) In Licentiate Theses in Mathematical Sciences 2025(2).
Abstract
The thesis is devoted to sharp embeddings from Soblolev spaces into Lebesque spaces in one dimension. The paper included in the thesis concerns the embedding from Sobolev spaces of functions that have square integrable derivatives of integer order k into the space of Lebesgue integrable functions (p=1). The main result is the sharp constant and the explicit extremal functions given by the Landau kernels. The result improves on the two-sided estimates obtained by Kalyabin in 2014. We survey the literature of the sharp Sobolev inequalities and discuss discrete analogues and possible extensions.
Please use this url to cite or link to this publication:
author
supervisor
organization
publishing date
type
Thesis
publication status
published
subject
keywords
Sobolev inequalities
in
Licentiate Theses in Mathematical Sciences
volume
2025
issue
2
pages
50 pages
publisher
Lund University (Media-Tryck)
ISSN
1404-028X
ISBN
978-91-8104-685-4
978-91-8104-686-1
language
English
LU publication?
yes
id
4ed4d542-f26b-4f95-ba65-c03962d7ebac
date added to LUP
2025-10-14 10:10:12
date last changed
2025-11-20 03:38:52
@misc{4ed4d542-f26b-4f95-ba65-c03962d7ebac,
  abstract     = {{The thesis is devoted to sharp embeddings from Soblolev spaces into Lebesque spaces in one dimension. The paper included in the thesis concerns the embedding from Sobolev spaces of functions that have square integrable derivatives of integer order k into the space of Lebesgue integrable functions (p=1). The main result is the sharp constant and the explicit extremal functions given by the Landau kernels. The result improves on the two-sided estimates obtained by Kalyabin in 2014. We survey the literature of the sharp Sobolev inequalities and discuss discrete analogues and possible extensions.<div/>}},
  author       = {{Hindov, Raul}},
  isbn         = {{978-91-8104-685-4}},
  issn         = {{1404-028X}},
  keywords     = {{Sobolev inequalities}},
  language     = {{eng}},
  month        = {{10}},
  note         = {{Licentiate Thesis}},
  number       = {{2}},
  publisher    = {{Lund University (Media-Tryck)}},
  series       = {{Licentiate Theses in Mathematical Sciences}},
  title        = {{A left inverse approach to sharp Sobolev inequalities}},
  url          = {{https://lup.lub.lu.se/search/files/230054649/2025-08-27-Raul_thesis.pdf}},
  volume       = {{2025}},
  year         = {{2025}},
}