加权的Hardy空间和面积积分的加权模不等式

本文建立了具有高阶消失矩的加权的原子Ｈａｒｄｙ空间，证明了０＜Ｐ＜＝１时面积积分的双向加权模不等式。     

Weighted Norm Inequalities on Graphs

Let (??,??) be an infinite graph endowed with a reversible Markov kernel p and let P be the corresponding operator. We also consider the associated discrete gradient ?. We assume that ?? is doubling, a uniform lower bound for p(x,y) when p(x,y)>0, and gaussian upper estimates for the iterates of p. Under these conditions (and in some cases assuming further some Poincaré inequality) we study the comparability of (I?P)^1/2 f and ?f in Lebesgue spaces with Muckenhoupt weights. Also, we establish weighted norm inequalities for a Littlewood?CPaley?CStein square function, its formal adjoint, and commutators of the Riesz transform with bounded mean oscillation functions.     

Some Weighted Norm Inequalities on Manifolds

Let M be a complete non-compact Riemannian manifold satisfying the volume doubling property and the Gaussian upper bounds. Denote by △ the Laplace-Beltrami operator and by ▽ the Riemannian gradient. In this paper, the author proves the weighted reverse inequality ‖△ 1/2 f‖Lp(ω) ≤ C‖|▽f|‖Lp(ω), for some range of p determined by M and w. Moreover, a weak type estimate is proved when p = 1. Some weighted vector-valued inequalities are also established.     

Weighted Norm Inequalities for Spectral Multipliers on Graphs

Let Γ be a graph endowed with a reversible Markov kernel p, whose associated operator P is defined by \(Pf(x) = {\sum }_{y} p(x, y)f(y)\). We assume that the kernels p_n(x, y) associated to Pⁿ satisfy Gaussian upper bounds but do not assume they satisfy the Hölder continuity property and the temporal regularity. Denote by L = I ? P the discrete Laplacian on Γ. This article shows the weighted weak type (1, 1) estimates and the weighted L^p norm inequalities for the spectral multipliers of L. We also obtain the weighted L^p norm inequalities for the commutators of the spectral multipliers of L with BMO functions which are new even for the unweighted case.     

Weighted Grand Lebesgue Space with a Mixed Norm and Integral Operators

Doklady Mathematics - Weighted grand Lebesgue spaces with mixed norms are introduced, and criteria for the boundedness of strong maximal functions and Riesz transforms in these spaces are given.     

Weighted Norm Inequalities for Singular Integral Operators

For a Calderón-Zygmund singular integral operator T,we show that the following weighted inequality holds     

位势型算子的加权不等式

Let Ф be a non-negative locally integrable function on R^n and satisfy some weak growth conditions, define the potential type operator TФ by TФf（x）=∫R^n Ф（x-y）f（y）dy. The aim of this paper is to give several strong type and weak type weighted norm inequalities for the potential type operator TФ.     

Weighted Norm Inequalities for the Hardy Operator

In this paper.a characterizationis,obtained for those pairs of weight funetions on(0=∞) for which the Hardy operator Pf(x)=f(t)dt is bounded from (μ) to ,0相似文献   

Weighted Lorentz Norm Inequalities for Riemann-Liouville Fractional Integra

§１．ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔＫ（ｘ，ｙ）≥０ｂｅｄｅｆｉｎｅｄｏｎ｛（ｘ，ｙ）∈Ｒ＋×Ｒ＋：ｘ＞ｙ｝，ａｎｄμ，νｂｅｔｈｅｐｏｓｉｔｉｖｅＢｏｒｅｌｍｅａｓｕｒｅｓｏｎＲ＋．ＷｅｄｅｆｉｎｅｔｈｅｉｎｔｅｇｒａｌｏｐｅｒａｔｏｒＴｆ（ｘ）＝...     

Weighted Norm Inequalities for the Local Sharp Maximal Function

A weighted norm inequality for the local sharp maximal function M^# f is proved. Our main result along with the extrapolation theorem by D. Cruz-Uribe and C. Perez is applied to obtaining several new weighted norm inequalities for maximal functions and singular integrals. Several open problems are given.     

Norm Inequalities for Fractional Integral Operators on Generalized Weighted Morrey Spaces

Considering a class of operators which include fractional integrals related to operators with Gaussian kernel bounds,the fractional integral operators with rough kernels and fractional maximal operators with rough kernels as special cases,we prove that if these operators are bounded on weighted Lebesgue spaces and satisfy some local pointwise control,then these operators and the commutators of these operators with a BMO functions are also bounded on generalized weighted Morrey spaces.     

多线性向量值奇异积分极大算子的加权不等式

本文研究向量值奇异积分极大多线性交换子的性质,得到该算子的加权估计及加权弱型估计,作为该估计的推论可知算子T_(q,(?))~*在L~p(ω)上有界,其中ω∈A_p。当ω∈A_1时,满足加权L(logL)~(1/r)型估计。     

变量核奇异积分和分数次微分加权范不等式

用T和D^γ（0 ≤ γ ≤ 1）分别表示变量核奇异积分和分数次微分算子.T^*和T^#分别为T的共轭算子及拟共轭算子.利用球调和多项式展式,本文得到了TD^γ-D^γT和（T^*-T^#）D^γ在?^q,λ_ω（Rⁿ）上的有界性.同时也得到了变量核奇异积分的积T₁T₂和拟积T₁°T₂的加权范不等式.     

Weighted Norm Inequalities for General Maximal Operators and Approach Regions

We find a characterization of a two-weight norm inequality for a maximal operator and we obtain, as a consequence, strong type estimates for the maximal function over general approach regions.     

Sharp Norm Estimates for Weighted Bergman Projections in the Mixed Norm Spaces

In this paper, we show that the norm of the Bergman projection on L^p,q-spaces in the upper half-plane is comparable to csc(π/q). Then we extend this result to a more general class of domains, known as the homogeneous Siegel domains of type II.     

Mixed Norm Inequalities for Directional Operators Associated to Potentials

We study mixed norm inequalities for directional operators which appear applying the method of rotations to homogeneous operators with variable kernel and with the homogeneity of Riesz potentials. The results are sharp for a range of values of the parameter and for all its values when the inequalities are restricted to radial functions.     

一类多线性奇异积分算子的加权估计

In this paper, weighted estimates with general weights are established for the multilinear singular integral operator defined by TAf(x) = p. v.RnΩ(x- y)|x- y|n+1 A(x)- A(y)- A(y)(x- y) f(y)dy,where Ω is homogeneous of degree zero, has vanishing moment of order one, and belongs to Lipγ(Sn-1) with γ∈(0, 1], A has derivatives of order one in BMO(Rn).     

New Weighted Norm Inequalities for Certain Classes of Multilinear Operators on Morrey-type Spaces

Applying the new class of multiple weights A_p~θ, we establish some weighted norm inequalities for certain classes of multilinear operators in the Morrey-type spaces. In addition, the new multiple weighted norm inequalities for multilinear commutators of T with the new BMO functions BMO_θ are also obtained.