In this paper,we obtain a parameter type logarithmic Sobolev inequality with weight and a modified parameter type logarithmic Sobolev inequality with weight on Euclidean space based on the parameter type logarithmic C...In this paper,we obtain a parameter type logarithmic Sobolev inequality with weight and a modified parameter type logarithmic Sobolev inequality with weight on Euclidean space based on the parameter type logarithmic Caffarelli-Kohn-Nirenberg inequality on Euclidean space,respectively.By virtue of the convexity of a special function equivalent to a logarithmic Hölder inequality,and combining the Sobolev inequality and Gagliardo-Nirenberg inequality on Hörmander's vector fields,we also derive a logarithmic Sobolev inequality and a parameter type logarithmic Gagliardo-Nirenberg inequality on Hörmander's vector fields,respectively.In addition,a parameter type logarithmic Sobolev inequality on Hörmander's vector fields is given by suitable stretching transformation.展开更多
基金Supported by the National Natural Science Foundation of China(12261053)the Special Basic Cooperative Research Programs of Yunnan Provincial Undergraduate Universities Association(2019FH001-078,202101BA070001-132)Introduction of Talents Research Project of Kunming University(XJ20210020,YJL20019)。
基金National Natural Science Foundation of China(Grant No.12261053)the project Science and Technology Project of Yunnan Province,Key Technology Projects in Yunnan Province(Grant No.202302AF080003)+1 种基金the Special Basic Cooperative Research Programs of Yunnan Provincial Undergraduate Universities Association(Grant Nos.202401BA070001-110,202301BA070001-002 and 202101BA070001-132)the Scientific Research Fund of Education Department of Yunnan Province(Grant Nos.2024Y775,2024Y776,2025Y1076 and 2024J0775).
文摘In this paper,we obtain a parameter type logarithmic Sobolev inequality with weight and a modified parameter type logarithmic Sobolev inequality with weight on Euclidean space based on the parameter type logarithmic Caffarelli-Kohn-Nirenberg inequality on Euclidean space,respectively.By virtue of the convexity of a special function equivalent to a logarithmic Hölder inequality,and combining the Sobolev inequality and Gagliardo-Nirenberg inequality on Hörmander's vector fields,we also derive a logarithmic Sobolev inequality and a parameter type logarithmic Gagliardo-Nirenberg inequality on Hörmander's vector fields,respectively.In addition,a parameter type logarithmic Sobolev inequality on Hörmander's vector fields is given by suitable stretching transformation.
