Change search
ReferencesLink to record
Permanent link

Direct link
Some new results concerning Schur multipliers and duality results between Bergman-Schatten and little Bloch spaces
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
2009 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

This Licentiate thesis consists of an introduction and three papers, which deal with some spaces of infinite matrices. In the introduction we give an overview of the area that serves as a frame for the rest of the thesis.In Paper 1 we introduce the space $B_w(\ell^2)$ of linear (unbounded) operators on $\ell^2$ which map decreasing sequences from $\ell^2$ into sequences from $\ell^2$ and we find some classes of operators belonging either to $B_w(\ell^2)$ or to the space of all Schur multipliers on $B_w(\ell^2)$.In Paper 2 we further continue the study of the space $B_w(\ell^p)$ in the range $1 <\infty$. In particular, we characterize the upper triangular positive matrices from $B_w(\ell^p)$.In Paper 3 we prove a new characterization of the Bergman-Schatten spaces $L_a^p(D,\ell^2)$, the space of all upper triangular matrices such that $\|A(\cdot)\|_{L^p(D,\ell^2)}<\infty$, where \[\|A(r)\|_{L^p(D,\ell^2)}=\left(2\int_0^1\|A(r)\|^p_{C_p}rdr\right)^\frac{1}{p}. \]This characterization is similar to that for the classical Bergman spaces. We also prove a duality between the little Bloch space and the Bergman-Schatten classes in the case of infinite matrices.

Place, publisher, year, edition, pages
Luleå: Luleå tekniska universitet, 2009. , 9 p.
Licentiate thesis / Luleå University of Technology, ISSN 1402-1757
Research subject
URN: urn:nbn:se:ltu:diva-17166Local ID: 1fe59bb0-3003-11de-bd0f-000ea68e967bISBN: 978-91-86233-38-9OAI: diva2:990165
Godkänd; 2009; 20090423 (livmar); LICENTIATSEMINARIUM Ämnesområde: Matematik/Mathematics Examinator: Professor Lars-Erik Persson, Luleå tekniska universitet Tid: Tisdag den 2 juni 2009 kl 10.15 Plats: D 2214, Luleå tekniska universitetAvailable from: 2016-09-29 Created: 2016-09-29Bibliographically approved

Open Access in DiVA

fulltext(516 kB)0 downloads
File information
File name FULLTEXT01.pdfFile size 516 kBChecksum SHA-512
Type fulltextMimetype application/pdf

Search in DiVA

By author/editor
Marcoci, Liviu-Gabriel
By organisation
Mathematical Science

Search outside of DiVA

GoogleGoogle Scholar
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

ReferencesLink to record
Permanent link

Direct link