Sobolev type inequalities for general symmetric forms

Feng-Yu Wang
2000 Proceedings of the American Mathematical Society  
A general version of the Sobolev type inequality, including both the classical Sobolev inequality and the logarithmic Sobolev one, is studied for general symmetric forms by using isoperimetric constants. Some necessary and sufficient conditions are presented as results. The main results are illustrated by two examples of birth-death processes.
doi:10.1090/s0002-9939-00-05471-x fatcat:o765vvh3cfc2tffjlcjgp57nmy