Dr. Hirokazu Maruoka, Yukawa Institute for Theoretical Physics, Kyoto University.

Language: English.

Abstract: It is well-known that functions in critical Sobolev spaces embed into the space of functions of bounded mean oscillation (BMO) originating in the work of John and Nirenberg. Less well-known is the fact that they actually embed into BMO on subspaces of every smaller dimension. In this talk we introduce a class of spaces which are finer targets of these critical Sobolev embeddings than BMO that capture this phenomena, which we term beta-dimensional BMO. Interestingly, these spaces also gives an answer to the question of which BMO functions admit restrictions in BMO of subspaces. The key tool is a capacitary analogue of the John-Nirenberg inequality for the Hausdorff content, obtained recently in a joint work with You-Wei Chen.

What is GPSS Group?
GPSS Group is Tokyo based and engaged in a wide range of energy businesses including solar, wind, geothermal, hydro, and biogas, as well as a variety of other businesses to realize a sustainable society. We consider the gifts of nature such: as water, wind, and heat, which all exist in the local regions as the "local commons." To create a sustainable society together with the local communities, we utilize these potentials that are naturally replenished. 

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