12.01.2016
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Dissertation news

Dissertation: 23.1.16 Maximal operators and capacities in metric spaces (Nuutinen)

Time:

23.1.2016 12:00 — 15:00


Location: Seminaarinmaki, H320
M.Sc. Juho Nuutinen defends his doctoral dissertation in Mathematics ”Maximal operators and capacities in metric spaces”. Opponent Adjunct Professor Petteri Harjulehto (University of Turku and custos University Lecturer Heli Tuominen (University of Jyväskylä). The doctoral dissertation is held in Finnish.

Juho NuutinenM.Sc. Juho Nuutinen defends his doctoral dissertation in Mathematics ”Maximal operators and capacities in metric spaces”. Opponent Adjunct Professor Petteri Harjulehto (University of Turku and custos University Lecturer Heli Tuominen (University of Jyväskylä). The doctoral dissertation is held in Finnish.

In the thesis, we study different maximal operators and capacities in the setting of a doubling metric measure space. We study the mapping properties, such as boundedness and continuity, of different maximal operators in various function spaces. Maximal operators are central tools in geometric analysis, harmonic analysis and in the theory of partial differential equations. Especially in applications concerning Sobolev functions and partial differential equations, it is important to know how maximal operators preserve the regularity properties of functions. The capacity of a set measures its size from the point of view of potential theory. For example, in the study of removable singularities and boundary regularity criteria, the results are usually expressed in terms of capacities. We study metric space versions of the Riesz and Besov capacities. Main results are capacity estimates in terms of a corresponding modified Hausdorff content.

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Juho Nuutinen

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juho.nuutinen@jyu.fi