Artur Słabuszewski
supervisor: Przemysław Górka
We consider a fractional Slobodeckij space defined on a metric-measure space (`X, d, μ`). During the talk I will present that under some additional assumption, there is an equivalence between boundedness of the Sobolev embedding operator and the lower regularity of `μ`. Moreover, I will discuss compactness of `L^p` embedding operator and relation with Hajłasz-Sobolev spaces. The talk is based on a joint work with Przemysław Górka.
P.Górka, A. Słabuszewski, Embedding of fractional Sobolev spaces is equivalent to regularity of the measure, Studia Mathematica, in press.
P.Górka, A. Słabuszewski, Embeddings of the fractional Sobolev spaces on metric-measure spaces, Nonlinear Analysis, 2022.