Korevaar-Schoen p-energy forms and associated p-energy measures on fractals

We construct good p-energy forms on metric measure spaces as pointwise subsequential limits of Besov-type p-energy functionals under certain geometric/analytic conditions. Such forms are often called Korevaar-Schoen p-energy forms in the literature. As an advantage of our approach, the associated p-energy measures are obtained and investigated. We also prove that our construction is applicable to the settings of Kigami [Mem. Eur. Math. Soc. 5 (2023)] and Cao-Gu-Qiu [Adv. Math. 405 (2022), no. 108517], yields Korevaar-Schoen p-energy forms comparable to the p-energy forms constructed in these papers, and can be further modified in the case of self-similar sets to obtain self-similar p-energy forms keeping most of the good properties of Korevaar-Schoen ones.