A generalized weighted Hardy-Ces\`{a}ro operator, and its commutator on weighted LpL^p and BMO spaces

In this paper, we introduce a new weighted Hardy-Ces\`{a}ro operator defined by $U_{\psi,s}f(x)=\int\limits_0^1 f(s(t)\cdot x) \psi(t)dt$, which is associated to the parameter curve $s(t,x)=s(t)x$. Under certain conditions on $s(t)$ and on an absolutely homogeneous weight function $\omega$, we characterize the weight function $\psi$ such that $U_{\psi,s}$ is bounded on $L^p(\omega)$, $BMO(\omega)$. The corresponding operator norms are worked out too. These results extend the ones of Jie Xiao \cite{xiao}. We also give a sufficient and a necessary condition on the weight function $\psi$, which ensure the boundedness of the commutators of operator $U_{\psi,s}$ on $L^p(\omega)$ with symbols in $BMO(\omega)$.Comment: 19 page

Context Learning for Bone Shadow Exclusion in CheXNet Accuracy Improvement

Chest X-ray examination plays an important role in lung disease detection. The more accuracy of this task, the more experienced radiologists are required. After ChestX-ray14 dataset containing over 100,000 frontal-view X-ray images of 14 diseases was released, several models were proposed with high accuracy. In this paper, we develop a work flow for lung disease diagnosis in chest X-ray images, which can improve the average AUROC of the state-of-the-art model from 0.8414 to 0.8445. We apply image preprocessing steps before feeding to the 14 diseases detection model. Our project includes three models: the first one is DenseNet-121 to predict whether a processed image has a better result, a convolutional auto-encoder model for bone shadow exclusion is the second one, and the last is the original CheXNet.Comment: KSE 2018 long pape

Vector valued maximal Carleson type operators on the weighted Lorentz spaces

In this paper, by using the idea of linearizing maximal op-erators originated by Charles Fefferman and the TT* method of Stein-Wainger, we establish a weighted inequality for vector valued maximal Carleson type operators with singular kernels proposed by Andersen and John on the weighted Lorentz spaces with vector-valued functions

Multilinear Hausdorff operators on some function spaces with variable exponent

The aim of the present paper is to give necessary and sufficient conditions for the boundedness of a general class of multilinear Hausdorff operators that acts on the product of some weighted function spaces with variable exponent such as the weighted Lebesgue, Herz, central Morrey and Morrey-Herz type spaces with variable exponent. Our results improve and generalize some previous known results.Comment: 36 page

Weighted estimates for commutators of multilinear Hausdorff operators on variable exponent Morrey-Herz type spaces

In this paper, we establish the boundedness of the commutators of multilinear Hausdorff operators on the product of some weighted Morrey-Herz type spaces with variable exponent with their symbols belong to both Lipschitz space and central BMO space. By these, we generalize and strengthen some previous known results.Comment: arXiv admin note: text overlap with arXiv:1709.0818

Weighted Lebesgue and central Morrey estimates for p-adic multilinear Hausdorff operators and its commutators

In this paper, we establish the sharp boundedness of p-adic multilinear Hausdorff operators on the product of Lebesgue and central Morrey spaces associated with both power weights and Muckenhoupt weights. Moreover, the boundedness for the commutators of p-adic multilinear Hausdorff operators on the such spaces with symbols in central BMO space is also obtained

Weighted norm inequalities for rough Hausdorff operator and its commutators on the Heisenberg group

The aim of this paper is to study the sharp bounds of rough Hausdorff operators on the product of Herz, central Morrey and Morrey-Herz spaces with both power weights and Muckenhoupt weights on the Heisenberg group. Especially, by applying the block decomposition of the Herz space, we obtain the boundedness of rough Hausdorff operator in the case 0 < p < 1. In addition, the boundedness for the commutators of rough Hausdorff operators on such spaces with symbols in weighted central BMO space is also established.Comment: added Nguyen Minh Chuong as the first autho

Weighted Morrey-Herz space estimates for rough Hausdorff operator and its commutators

In this paper, we give necessary and sufficient conditions for the boundedness of rough Hausdorff operators on Herz, Morrey and Morrey-Herz spaces with absolutely homogeneous weights. Especially, the estimates for operator norms in each case are worked out. Moreover, we also establish the boundedness of the commutators of rough Hausdorff operators on the such spaces with their symbols belonging to Lipschitz space

Maximal operators and singular integrals on the weighted Lorentz and Morrey spaces

In this paper, we first give some new characterizations of Muckenhoupt type weights through establishing the boundedness of maximal operators on the weighted Lorentz and Morrey spaces. Secondly, we establish the boundedness of sublinear operators including many interesting in harmonic analysis and its commutators on the weighted Morrey spaces. Finally, as an application, the boundedness of strongly singular integral operators and commutators with symbols in BMO space are also given

Some estimates for p-adic rough multilinear Hausdorff operators and commutators on weighted Morrey-Herz type spaces

The aim of this paper is to introduce and study the boundedness of a new class of p-adic rough multilinear Hausdorff operators on the product of Herz, central Morrey and Morrey-Herz spaces with power weights and Muckenhoupt weights. We also establish the boundedness for the commutators of p-adic rough multilinear Hausdorff operators on the weighted spaces with symbols in central BMO space.Comment: arXiv admin note: text overlap with arXiv:1810.0689