In this paper,two new functions are introduced to depict the Jamison weighted sum of random variables instead using the common methods,their properties and relationships are system- atically discussed.We also analysed...In this paper,two new functions are introduced to depict the Jamison weighted sum of random variables instead using the common methods,their properties and relationships are system- atically discussed.We also analysed the implication of the conditions in previous papers.Then we apply these consequences to B-valued random variables,and greatly improve the original results of the strong convergence of the general Jamison weighted sum.Furthermore,our discussions are useful to the corresponding questions of real-valued random variables.展开更多
设1<p2,0<α1,X是p一致可光滑空间的Banach空间,则对每个X值拟鞅f=(fn)n≥0∈pHασ(X)存在分解fn=sum form k∈Z to μkank(n≥0),并且‖f‖pHασ(X)+‖R(f)‖α～inf(sum form k∈Z to μkα)1/α,这里ak=(ank)n5≥0(k∈Z)是一...设1<p2,0<α1,X是p一致可光滑空间的Banach空间,则对每个X值拟鞅f=(fn)n≥0∈pHασ(X)存在分解fn=sum form k∈Z to μkank(n≥0),并且‖f‖pHασ(X)+‖R(f)‖α～inf(sum form k∈Z to μkα)1/α,这里ak=(ank)n5≥0(k∈Z)是一列(1,α,∞;p)拟鞅原子,并且在L1中收敛,supk∈Z‖ak*‖α<∞,(μk)k∈Z∈lα是非负实数列.对于拟鞅空间pHαS(X)和qKα(X)成立类似的结果.此外,利用拟鞅原子分解定理,证明了几个拟鞅不等式.展开更多
基金Research supported by National Science Foundation of China(No.10071081)special financial support of Chinese Academy of Sciences
文摘In this paper,two new functions are introduced to depict the Jamison weighted sum of random variables instead using the common methods,their properties and relationships are system- atically discussed.We also analysed the implication of the conditions in previous papers.Then we apply these consequences to B-valued random variables,and greatly improve the original results of the strong convergence of the general Jamison weighted sum.Furthermore,our discussions are useful to the corresponding questions of real-valued random variables.
文摘设1<p2,0<α1,X是p一致可光滑空间的Banach空间,则对每个X值拟鞅f=(fn)n≥0∈pHασ(X)存在分解fn=sum form k∈Z to μkank(n≥0),并且‖f‖pHασ(X)+‖R(f)‖α～inf(sum form k∈Z to μkα)1/α,这里ak=(ank)n5≥0(k∈Z)是一列(1,α,∞;p)拟鞅原子,并且在L1中收敛,supk∈Z‖ak*‖α<∞,(μk)k∈Z∈lα是非负实数列.对于拟鞅空间pHαS(X)和qKα(X)成立类似的结果.此外,利用拟鞅原子分解定理,证明了几个拟鞅不等式.
