摘要
Let （Xt）t≥0 be a symmetric strong Markov process generated by non-local regular Dirichlet form （D, （D）） as follows：where J（x, y） is a strictly positive and symmetric measurable function on Rd × Rd. We study the intrinsic hypercontractivity, intrinsic supercontractivity, and intrinsic ultracontractivity for the Feynman-Kac semigroup
Let （Xt）t≥0 be a symmetric strong Markov process generated by non-local regular Dirichlet form （D, （D）） as follows：where J（x, y） is a strictly positive and symmetric measurable function on Rd × Rd. We study the intrinsic hypercontractivity, intrinsic supercontractivity, and intrinsic ultracontractivity for the Feynman-Kac semigroup
基金
The authors would like to thank Professor Mu-Fa Chen and Professor Feng-Yu Wang for introducing them the field of functional inequalities when they studied in Beijing Normal University, and for their continuous encouragement and great help in the past few years. The authors are also indebted to the referees for valuable comments on the draft. This work was supported by the National Natural Science Foundation of China （Grant No. 11201073）, Japan Society for the Promotion of Science （No. 26.04021）, the Natural Science Foundation of Fujian Province （No. 2015J01003）, and the Program for Nonlinear Analysis and Its Applications （No. IRTL1206） （for Jian Wang）.
