Potential analysis

·Under the capacity density condition，we characterize uniform domains，inner uniform domains and John domains in terms of the boundary Hamack principle and estimates of harmonic measure.·We study the bounday behavior of non-integrable kernel and derive the Fatou type theorem and Littlewood type theorem.·We show the 3G-inequality for inner uniform domains。We construct a domain whose Martin boundary and topological boundary coincide，and yet the Cranston-McConnell inequality，and as a result，the 3G-inequality fail to hold in case the dimension is greater than or equal3。·We show the equivalence between the boundary Hamack principle and the Carleson estimate。·For a smooth doimain in the Euclid space。We show the boundary Harnack principle for p-harmonic func-tion。·We give the Carleson estomates for p-harmonic functions.·We give conditions for the p-Dirichlet solution of a Holder continuos boundary function to be Hoder continuos up tp the boundary。·We study the Martin boundary of a John domain。By the John constant，we estimate the number of minimal Martin boundary points over a topological boundary。

・Under the capacity density condition, we characterize uniform domains, inner uniform domains and John domains in terms of the boundary Hamack principle and estimates of harmonic measure.・We study the bounday behavior of non-integrable kernel and derive the Fatou type theorem and Littlewood type theorem.・We show the 3G-inequality for inner uniform domains. We construct a domain whose Martin boundary and topological boundary coincide, and yet the Cranston-McConnell inequality, and as a result, the 3G- inequality fail to hold in case the dimension is greater than or equal 3.・We show the equivalence between the boundary Hamack principle and the Carleson estimate.・For a smooth doimain in the Euclid space. we show the boundary Harnack principle for p-harmonic func- tion.・We give the Carleson estomates for p-harmonic functions.・We give conditions for the p-Dirichlet solution of a Holder continuos boundary function to be Hoder continuos up tp the boundary.・We study the Martin boundary of a John domain. By the John constant, we estimate the number of minimal Martin boundary points over a topological boundary.