# AbstractsMathematics

by Mahdi Hormozi

Institution: University of Gothenburg / Göteborgs Universitet 2015 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 02/05/2017 2132878 http://hdl.handle.net/2077/39305

## Abstract

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-Λ-variation function is given and Helly's selection principle for Λ 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 Λ BV(p) is found. In paper II, a characterization of the inclusion of Waterman-Shiba classes into Hωq 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 :Λ BV(p): into generalized Wiener classes of functions BV(q;,δ) 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 SD8n. 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 , it is possible that V_φ(G) has no o-basis when φ is a linear Brauer character. Let vec{P}=(p1,dotsc,pm) with 1