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Topics on Harmonic analysis and Multilinear Algebra

Mahdi Hormozi (Institutionen för matematiska vetenskaper)
2015.
[Doktorsavhandling]

The present thesis consists of six different papers. Indeed, they treat three different research areas: function spaces, singular integrals and multilinear algebra. In paper I, a characterization of continuity of the $p$-$\Lambda$-variation function is given and Helly's selection principle for $\Lambda BV^{(p)}$ functions is established. A characterization of the inclusion of Waterman-Shiba classes into classes of functions with given integral modulus of continuity is given. A useful estimate on the modulus of variation of functions of class $\Lambda BV^{(p)}$ is found. In paper II, a characterization of the inclusion of Waterman-Shiba classes into $H_{\omega}^{q}$ is given. This corrects and extends an earlier result of a paper from 2005. In paper III, the characterization of the inclusion of Waterman-Shiba spaces $\:\Lambda BV^{(p)}\:$ into generalized Wiener classes of functions $BV(q;\,\delta)$ is given. It uses a new and shorter proof and extends an earlier result of U. Goginava. In paper IV, we discuss the existence of an orthogonal basis consisting of decomposable vectors for all symmetry classes of tensors associated with Semi-dihedral groups $SD_{8n}$. In paper V, we discuss o-bases of symmetry classes of tensors associated with the irreducible Brauer characters of the Dicyclic and Semi-dihedral groups. As in the case of Dihedral groups [46], it is possible that $V_\phi(G)$ has no o-basis when $\phi$ is a linear Brauer character. Let $\vec{P}=(p_1,\dotsc,p_m)$ with $1

Nyckelord: Generalized bounded variation, Helly's theorem, Modulus of variation, Generalized Wiener classes, Symmetry classes of tensors, Orthogonal basis, Brauer symmetry classes of tensors, Multilinear singular integrals, weighted norm inequalities, weighted bounds, local mean oscillation, Lerner's formula



Denna post skapades 2016-02-22.
CPL Pubid: 232300

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaperInstitutionen för matematiska vetenskaper (GU)

Ämnesområden

Matematik

Chalmers infrastruktur

Examination

Datum: 2015-10-22
Lokal: Thursday 22th of October 2015, at 13:15 in room Pascal, Department of Mathematical Sciences, Chalmers Tvärgata 3