Heli Tuominen (University of Jyväskylä)
Orlicz-Sobolev spaces on metric measure spaces
Abstract.
In the talk, I will define Orlicz-Sobolev spaces on metric measure spaces using weak upper gradients and discuss the basic properties of the spaces. The definition is a generalization of Newtonian spaces, Sobolev spaces on metric measure spaces; instead of being p-integrable, functions and upper gradients are supposed to be in an Orlicz space. New tools, such as modulus, capacity, and Poincaré-type inequalities, connected to Young function are needed for these spaces. The Orlicz-Sobolev space is always a Banach space and its functions are absolutely continuous on almost all curves. If the Young function that defines the Orlicz space is doubling, then the Orlicz-Sobolev space has more important properties, for example density of bounded functions and existence of a minimal weak upper gradient. If the underlying metric space supports a Poincaré-type inequality, then Lipschitz functions are dense both in norm and "in the Lusin sense". The talk is based on my PhD thesis.

Back to talks