In this note,we introduce and study a new kind of generalized Cesaro operator,C_(μ),induced by a positive Borel measure μ on(0,1)between Dirichlet-type spaces.We characterize the measures μ for which Cμis bounded(...In this note,we introduce and study a new kind of generalized Cesaro operator,C_(μ),induced by a positive Borel measure μ on(0,1)between Dirichlet-type spaces.We characterize the measures μ for which Cμis bounded(compact)from one Dirichlet-type space,Da,into another one,D_(β).展开更多
This paper deals with a general class of weighted multilinear Hardy-Cesaro op- erators that acts on the product of Lebesgue spaces and central Morrey spaces. Their sharp bounds are also obtained. In addition, we obtai...This paper deals with a general class of weighted multilinear Hardy-Cesaro op- erators that acts on the product of Lebesgue spaces and central Morrey spaces. Their sharp bounds are also obtained. In addition, we obtain sufficient and necessary conditions on weight functions so that the commutators of these weighted multilinear Hardy-Cesaro oper- ators （with symbols in central BMO spaces） are bounded on the product of central Morrey spaces. These results extends known results on multilinear Hardy operators.展开更多
A new constant C(X)for any Banach space X is introduced.It is proved that C(X)<2 implies the weak Banach–Saks property for the space X:In particular,C(cesp)is found for Cesàro sequence space cesp(1<p<∞...A new constant C(X)for any Banach space X is introduced.It is proved that C(X)<2 implies the weak Banach–Saks property for the space X:In particular,C(cesp)is found for Cesàro sequence space cesp(1<p<∞).Moreover,it is shown that the space cesp(1<p<∞)has property(β).展开更多
基金supported by National Natural Science Foundation of China(11501157)supported by National Natural Science Foundation of China(12061022)the foundation of Guizhou Provincial Science and Technology Department(20177337 and 20175726)。
文摘In this note,we introduce and study a new kind of generalized Cesaro operator,C_(μ),induced by a positive Borel measure μ on(0,1)between Dirichlet-type spaces.We characterize the measures μ for which Cμis bounded(compact)from one Dirichlet-type space,Da,into another one,D_(β).
基金supported by Vietnam National Foundation for Science and Technology Development(101.02-2014.51)
文摘This paper deals with a general class of weighted multilinear Hardy-Cesaro op- erators that acts on the product of Lebesgue spaces and central Morrey spaces. Their sharp bounds are also obtained. In addition, we obtain sufficient and necessary conditions on weight functions so that the commutators of these weighted multilinear Hardy-Cesaro oper- ators （with symbols in central BMO spaces） are bounded on the product of central Morrey spaces. These results extends known results on multilinear Hardy operators.
文摘A new constant C(X)for any Banach space X is introduced.It is proved that C(X)<2 implies the weak Banach–Saks property for the space X:In particular,C(cesp)is found for Cesàro sequence space cesp(1<p<∞).Moreover,it is shown that the space cesp(1<p<∞)has property(β).
