To estimate the optimal constant in Hardy-type inequalities, some variational formulas and approximating procedures are introduced. The known basic estimates are improved considerably. The results are illustrated by t...To estimate the optimal constant in Hardy-type inequalities, some variational formulas and approximating procedures are introduced. The known basic estimates are improved considerably. The results are illustrated by typical examples. It is shown that the sharp factor is meaningful for each finite interval and a classical sharp model is re-examined.展开更多
As the extension of classical Hardy operator and Cesaro operator,Hausdorff operator plays an important role in the harmonic analysis,so it is significant to discuss the boundedness of this kind of operator on various ...As the extension of classical Hardy operator and Cesaro operator,Hausdorff operator plays an important role in the harmonic analysis,so it is significant to discuss the boundedness of this kind of operator on various function spaces.The article explores the boundedness of a kind of Hausdorff operators on Lebesgue spaces and calculates the optimal constants for the operators to be bounded on such spaces.In addition,the paper also obtains the necessary and sufficient for a kind of multilinear Hausdorff operators to be bounded on Lebesgue spaces and their optimal constants.展开更多
基金Supported by National Natural Science Foundation of China(Grant No.11131003)the "985" Project from the Ministry of Education in Chinathe Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions
文摘To estimate the optimal constant in Hardy-type inequalities, some variational formulas and approximating procedures are introduced. The known basic estimates are improved considerably. The results are illustrated by typical examples. It is shown that the sharp factor is meaningful for each finite interval and a classical sharp model is re-examined.
文摘As the extension of classical Hardy operator and Cesaro operator,Hausdorff operator plays an important role in the harmonic analysis,so it is significant to discuss the boundedness of this kind of operator on various function spaces.The article explores the boundedness of a kind of Hausdorff operators on Lebesgue spaces and calculates the optimal constants for the operators to be bounded on such spaces.In addition,the paper also obtains the necessary and sufficient for a kind of multilinear Hausdorff operators to be bounded on Lebesgue spaces and their optimal constants.
