Sobolev Embedding Theorems and Generalizations for Functions on a Metric Measure Space

摘要

Considering the metric case, we define an analog of the Sobolev space of functions with generalized derivatives of order greater than 1. The space of functions with fractional generalized derivatives is also treated. We prove generalizations of the Sobolev embedding theorems and Gagliardo-Nirenberg interpolation inequalities to the metric case.