Some new Lizorkin multiplier theorems for Fourier series and transforms
This Licentiate Thesis is devoted to the study of Fourier series and Fourier transform multipliers and contains three papers (papers A - C) together with an introduction, which put these papers into a general frame. In paper A a generalization of the Lizorkin theorem on Fourier multipliers is proved...
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Luleå tekniska universitet, Matematiska vetenskaper
2009
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ftluleatu:oai:DiVA.org:ltu-25710 2023-05-15T17:09:07+02:00 Some new Lizorkin multiplier theorems for Fourier series and transforms Sarybekova, Lyazzat 2009 application/pdf http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-25710 eng eng Luleå tekniska universitet, Matematiska vetenskaper Luleå Licentiate thesis / Luleå University of Technology, 1402-1757 http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-25710 urn:isbn:978-91-86233-40-2 Local ab9bd170-300c-11de-bd0f-000ea68e967b info:eu-repo/semantics/openAccess Mathematical Analysis Matematisk analys Licentiate thesis, comprehensive summary info:eu-repo/semantics/masterThesis text 2009 ftluleatu 2022-10-25T20:51:17Z This Licentiate Thesis is devoted to the study of Fourier series and Fourier transform multipliers and contains three papers (papers A - C) together with an introduction, which put these papers into a general frame. In paper A a generalization of the Lizorkin theorem on Fourier multipliers is proved. The proof is based on using the so-called net spaces and interpolation theorems. An example is given of a Fourier multiplier which satisfies the assumptions of the generalized theorem but does not satisfy the assumptions of the Lizorkin theorem.In paper B we prove and discuss a generalization and sharpening of the Lizorkin theorem concerning Fourier multipliers between $L_p$ and $L_q$. Some multidimensional Lorentz spaces and an interpolation technique (of Sparr type) are used as crucial tools in the proofs. The obtained results are discussed in the light of other generalizations of the Lizorkin theorem and some open questions are raised.Paper C deals with the Fourier series multipliers in the case with a regular system. This system is rather general. For example, trigonometrical systems, the Walsh system and all multiplicative system with bounded elements are regular. A generalization and sharpening of the Lizorkin type theorem concerning Fourier series multipliers between $L_p$ and $L_q$ in this general case is proved and discussed. Godkänd; 2009; 20090423 (lyazzat); LICENTIATSEMINARIUM Ämnesområde: Matematik/Mathematics Examinator: Professor Lars-Erik Persson, Luleå tekniska universitet Tid: Torsdag den 4 juni 2009 kl 10.00 Plats: D 2214, Luleå tekniska universitet Master Thesis Luleå Luleå Luleå University of Technology Publications (DiVA) Persson ENVELOPE(-58.400,-58.400,-64.200,-64.200) |
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Luleå University of Technology Publications (DiVA) |
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language |
English |
topic |
Mathematical Analysis Matematisk analys |
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Mathematical Analysis Matematisk analys Sarybekova, Lyazzat Some new Lizorkin multiplier theorems for Fourier series and transforms |
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Mathematical Analysis Matematisk analys |
description |
This Licentiate Thesis is devoted to the study of Fourier series and Fourier transform multipliers and contains three papers (papers A - C) together with an introduction, which put these papers into a general frame. In paper A a generalization of the Lizorkin theorem on Fourier multipliers is proved. The proof is based on using the so-called net spaces and interpolation theorems. An example is given of a Fourier multiplier which satisfies the assumptions of the generalized theorem but does not satisfy the assumptions of the Lizorkin theorem.In paper B we prove and discuss a generalization and sharpening of the Lizorkin theorem concerning Fourier multipliers between $L_p$ and $L_q$. Some multidimensional Lorentz spaces and an interpolation technique (of Sparr type) are used as crucial tools in the proofs. The obtained results are discussed in the light of other generalizations of the Lizorkin theorem and some open questions are raised.Paper C deals with the Fourier series multipliers in the case with a regular system. This system is rather general. For example, trigonometrical systems, the Walsh system and all multiplicative system with bounded elements are regular. A generalization and sharpening of the Lizorkin type theorem concerning Fourier series multipliers between $L_p$ and $L_q$ in this general case is proved and discussed. Godkänd; 2009; 20090423 (lyazzat); LICENTIATSEMINARIUM Ämnesområde: Matematik/Mathematics Examinator: Professor Lars-Erik Persson, Luleå tekniska universitet Tid: Torsdag den 4 juni 2009 kl 10.00 Plats: D 2214, Luleå tekniska universitet |
format |
Master Thesis |
author |
Sarybekova, Lyazzat |
author_facet |
Sarybekova, Lyazzat |
author_sort |
Sarybekova, Lyazzat |
title |
Some new Lizorkin multiplier theorems for Fourier series and transforms |
title_short |
Some new Lizorkin multiplier theorems for Fourier series and transforms |
title_full |
Some new Lizorkin multiplier theorems for Fourier series and transforms |
title_fullStr |
Some new Lizorkin multiplier theorems for Fourier series and transforms |
title_full_unstemmed |
Some new Lizorkin multiplier theorems for Fourier series and transforms |
title_sort |
some new lizorkin multiplier theorems for fourier series and transforms |
publisher |
Luleå tekniska universitet, Matematiska vetenskaper |
publishDate |
2009 |
url |
http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-25710 |
long_lat |
ENVELOPE(-58.400,-58.400,-64.200,-64.200) |
geographic |
Persson |
geographic_facet |
Persson |
genre |
Luleå Luleå |
genre_facet |
Luleå Luleå |
op_relation |
Licentiate thesis / Luleå University of Technology, 1402-1757 http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-25710 urn:isbn:978-91-86233-40-2 Local ab9bd170-300c-11de-bd0f-000ea68e967b |
op_rights |
info:eu-repo/semantics/openAccess |
_version_ |
1766065039291187200 |