Estimates for Discrete Hardy-type Operators in Weighted Sequence Spaces

• Main Author: Temirkhanova, Ainur
• Format: Doctoral or Postdoctoral Thesis
• Language: English
• Published: Luleå tekniska universitet, Matematiska vetenskaper 2015
• Subjects: Mathematical Analysis; Matematisk analys; Luleå
• Online Access: http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-18222

This PhD thesis consists of an introduction and eight papers, which deal with questions of the validity of some new discrete Hardy type inequalities in weighted spaces of sequences and on the cone of non-negative monotone sequences, and their applications. In the introduction we give an overview of the area that serves as a frame for the rest of the thesis. In particular, a short description of the development of Hardy type inequalities is given. In Paper 1 we find necessary and sufficient conditions on weighted sequences $\omega_i$, $i=1, 2,.,n-1$, $u$ and $v$, for which the operator $$ (S_{n}f)_i=\sum\limits_{k_1=1}^i\omega_{1,k_1}\cdots\sum\limits_{k_{n-1}=1}^{k_{n-2}} \omega_{n-1,k_{n-1}}\sum\limits_{j=1}^{k_{n-1}}f_j,~ i\geq 1,~(1) $$ is bounded from $l_{p,v}$ to $l_{q,u}$ for $1 Godkänd; 2015; 20151021 (aintem); Nedanstående person kommer att disputera för avläggande av teknologie doktorsexamen. Namn: Ainur Temirkhanova Ämne: Matematik/Mathematics Avhandling: Estimates for Discrete Hardy-type Operators in Weighted Sequence Spaces Opponent: Professor Mikhail Goldman, Dept of Nonlinear Analysis and Optimization, Peoples’Friendship University of Russia, Moscow, Russia. Ordförande: Professor Peter Wall, Avd för matematiska vetenskaper, Institutionen för teknikvetenskap och matematik, Luleå tekniska universitet, Luleå. Tid: Tisdag 8 december kl 10.00 Plats: E246, Luleå tekniska universitet