Inequalities involving heat potentials and Green functions. (English) Zbl 1363.31009

Watson, Neil A.

Math. Bohem. 140, No. 3, 313-318 (2015).

The author is concerned with inequalities for the heat potentials involving nonnegative measures on an arbitrary open set \(E\) whose support is a compact polar subset of \(E\). A particular attention is paid to the case where the support of the nonnegative measure reduces to a single point. In such a setting, the author establishes a formula for the associated Riesz measure.

Reviewer: Marius Ghergu (Dublin)

MSC:

31C05	Harmonic, subharmonic, superharmonic functions on other spaces
31C15	Potentials and capacities on other spaces
35K05	Heat equation

Keywords:

heat potentials; Green functions; Riesz measure