Here we consider some weighted logarithmic Sobolev inequalities which can be used in the theory of singular Riemanian manifolds.We give the necessary and sufficient conditions such that the 1-dimension weighted logari...Here we consider some weighted logarithmic Sobolev inequalities which can be used in the theory of singular Riemanian manifolds.We give the necessary and sufficient conditions such that the 1-dimension weighted logarithmic Sobolev inequality is true and obtain a new estimate on the entropy.展开更多
This paper deals with vanishing results for Lf^2 harmonic p-forms on complete metric measure spaces with a weighted p-Poincare inequality.Some results are without curvature assumptions for 1■p■n-1 and the others are...This paper deals with vanishing results for Lf^2 harmonic p-forms on complete metric measure spaces with a weighted p-Poincare inequality.Some results are without curvature assumptions for 1■p■n-1 and the others are with assumptions on lower bound of the m-Bakry-Emery Ricci curvature for p=1.These are weighted version for the corresponding results of the present author(J.Math.Anal.Appl.,2020,490).展开更多
The fractional maximal operator on homogeneous s pace (X,d,u)is defined as In this paper ,the su fficient and necessary conditions for the to be of weak type and extra weak type will be given.
In martingale setting, it has been shown that Ap weights can be factorized in terms of A 1 weights. This factorization benefits many problems very much. In this paper, the new class of RH ∞ plays the same role for RH...In martingale setting, it has been shown that Ap weights can be factorized in terms of A 1 weights. This factorization benefits many problems very much. In this paper, the new class of RH ∞ plays the same role for RH s , which makes the reverse Hlder inequalities hold with exponent s>1 , that the class A 1 does for A p class. Therefore, the Jones’ factorization theorem for A p weights was extended to include some information about the reverse Hlder classes. And it is the most convenient object in weight theory indeed.展开更多
Let m be an integer and T be an m-linear Calderón-Zygmund operator, u, v1,..., vm be weights. In this paper, the authors give some sufficient conditions on the weights (u, vk) with 1 ≤ k ≤ m, such that T is bou...Let m be an integer and T be an m-linear Calderón-Zygmund operator, u, v1,..., vm be weights. In this paper, the authors give some sufficient conditions on the weights (u, vk) with 1 ≤ k ≤ m, such that T is bounded from Lp1(Rn, v1) ×···× Lpm(Rn, vm) to Lp,∞(Rn, u).展开更多
We have pointed out in [1] that so far the L^2 norm inequalities with power weights for the Riesz means σ_R~δ(g)(x) of multiple Fourier integrals have been obtained only by Hirschman and J. L. Rubio de Francia respe...We have pointed out in [1] that so far the L^2 norm inequalities with power weights for the Riesz means σ_R~δ(g)(x) of multiple Fourier integrals have been obtained only by Hirschman and J. L. Rubio de Francia respectively:展开更多
基金Supported by the National Natural Science Foundation of China(11871436)。
文摘Here we consider some weighted logarithmic Sobolev inequalities which can be used in the theory of singular Riemanian manifolds.We give the necessary and sufficient conditions such that the 1-dimension weighted logarithmic Sobolev inequality is true and obtain a new estimate on the entropy.
基金Partially supported by National Science Foundation of China(11426195,11771377)Natural Science Foundation of Jiangsu Province(BK20191435)。
文摘This paper deals with vanishing results for Lf^2 harmonic p-forms on complete metric measure spaces with a weighted p-Poincare inequality.Some results are without curvature assumptions for 1■p■n-1 and the others are with assumptions on lower bound of the m-Bakry-Emery Ricci curvature for p=1.These are weighted version for the corresponding results of the present author(J.Math.Anal.Appl.,2020,490).
文摘The fractional maximal operator on homogeneous s pace (X,d,u)is defined as In this paper ,the su fficient and necessary conditions for the to be of weak type and extra weak type will be given.
基金Supported by the National Natural Science Foundation of China(19771063)
文摘In martingale setting, it has been shown that Ap weights can be factorized in terms of A 1 weights. This factorization benefits many problems very much. In this paper, the new class of RH ∞ plays the same role for RH s , which makes the reverse Hlder inequalities hold with exponent s>1 , that the class A 1 does for A p class. Therefore, the Jones’ factorization theorem for A p weights was extended to include some information about the reverse Hlder classes. And it is the most convenient object in weight theory indeed.
基金Supported by the National Natural Science Foundation of China (Grant No. 10971228)
文摘Let m be an integer and T be an m-linear Calderón-Zygmund operator, u, v1,..., vm be weights. In this paper, the authors give some sufficient conditions on the weights (u, vk) with 1 ≤ k ≤ m, such that T is bounded from Lp1(Rn, v1) ×···× Lpm(Rn, vm) to Lp,∞(Rn, u).
文摘We have pointed out in [1] that so far the L^2 norm inequalities with power weights for the Riesz means σ_R~δ(g)(x) of multiple Fourier integrals have been obtained only by Hirschman and J. L. Rubio de Francia respectively:
