This manuscript addresses Muckenhoupt Ap weight theory in connection to Mor- rey and BMO spaces. It is proved that a; belongs to Muckenhoupt Ap class, if and only if Hardy-Littlewood maximal function M is bounded from...This manuscript addresses Muckenhoupt Ap weight theory in connection to Mor- rey and BMO spaces. It is proved that a; belongs to Muckenhoupt Ap class, if and only if Hardy-Littlewood maximal function M is bounded from weighted Lebesgue spaces LP（w） to weighted Morrey spaces Mpq（ω） for 1 〈 q 〈 p 〈 ∞. As a corollary, if M is （weak） bounded on Mpq（ω）, then ω∈Ap. The Ap condition also characterizes the boundedness of the Riesz transform Rj and convolution operators Tε on weighted Morrey spaces. Finally, we show that ω∈Ap if and only if ω∈BMOp＇ （ω） for 1 ≤ p 〈 ∞ and 1/p ＋ 1/p＇ = 1.展开更多
In this work we prove the weighted Gevrey regularity of solutions to the incompressible Euler equation with initial data decaying polynomially at infinity. This is motivated by the well-posedness problem of vertical b...In this work we prove the weighted Gevrey regularity of solutions to the incompressible Euler equation with initial data decaying polynomially at infinity. This is motivated by the well-posedness problem of vertical boundary layer equation for fast rotating fluid. The method presented here is based on the basic weighted L;-estimate, and the main difficulty arises from the estimate on the pressure term due to the appearance of weight function.展开更多
Considering strip steel surface defect samples, a multi-class classification method was proposed based on enhanced least squares twin support vector machines （ELS-TWSVMs） and binary tree. Firstly, pruning region sam...Considering strip steel surface defect samples, a multi-class classification method was proposed based on enhanced least squares twin support vector machines （ELS-TWSVMs） and binary tree. Firstly, pruning region samples center method with adjustable pruning scale was used to prune data samples. This method could reduce classifierr s training time and testing time. Secondly, ELS-TWSVM was proposed to classify the data samples. By introducing error variable contribution parameter and weight parameter, ELS-TWSVM could restrain the impact of noise sam- ples and have better classification accuracy. Finally, multi-class classification algorithms of ELS-TWSVM were pro- posed by combining ELS-TWSVM and complete binary tree. Some experiments were made on two-dimensional data- sets and strip steel surface defect datasets. The experiments showed that the multi-class classification methods of ELS-TWSVM had higher classification speed and accuracy for the datasets with large-scale, unbalanced and noise samples.展开更多
基金supported by National Natural Science Foundation of China(Grant No.11661075)
文摘This manuscript addresses Muckenhoupt Ap weight theory in connection to Mor- rey and BMO spaces. It is proved that a; belongs to Muckenhoupt Ap class, if and only if Hardy-Littlewood maximal function M is bounded from weighted Lebesgue spaces LP（w） to weighted Morrey spaces Mpq（ω） for 1 〈 q 〈 p 〈 ∞. As a corollary, if M is （weak） bounded on Mpq（ω）, then ω∈Ap. The Ap condition also characterizes the boundedness of the Riesz transform Rj and convolution operators Tε on weighted Morrey spaces. Finally, we show that ω∈Ap if and only if ω∈BMOp＇ （ω） for 1 ≤ p 〈 ∞ and 1/p ＋ 1/p＇ = 1.
基金supported by NSF of China(11422106)the NSF of China(11171261)+1 种基金Fok Ying Tung Education Foundation(151001)supported by“Fundamental Research Funds for the Central Universities”
文摘In this work we prove the weighted Gevrey regularity of solutions to the incompressible Euler equation with initial data decaying polynomially at infinity. This is motivated by the well-posedness problem of vertical boundary layer equation for fast rotating fluid. The method presented here is based on the basic weighted L;-estimate, and the main difficulty arises from the estimate on the pressure term due to the appearance of weight function.
基金Item Sponsored by National Natural Science Foundation of China(61050006)
文摘Considering strip steel surface defect samples, a multi-class classification method was proposed based on enhanced least squares twin support vector machines （ELS-TWSVMs） and binary tree. Firstly, pruning region samples center method with adjustable pruning scale was used to prune data samples. This method could reduce classifierr s training time and testing time. Secondly, ELS-TWSVM was proposed to classify the data samples. By introducing error variable contribution parameter and weight parameter, ELS-TWSVM could restrain the impact of noise sam- ples and have better classification accuracy. Finally, multi-class classification algorithms of ELS-TWSVM were pro- posed by combining ELS-TWSVM and complete binary tree. Some experiments were made on two-dimensional data- sets and strip steel surface defect datasets. The experiments showed that the multi-class classification methods of ELS-TWSVM had higher classification speed and accuracy for the datasets with large-scale, unbalanced and noise samples.
