A new proof of the two weight norm inequality for the one-sided fractional maximal operator

We give a new proof of the two weight norm inequality for the one-sided, fractional maximal operator, , simplifying the original proof of Martín-Reyes and de la Torre.

     

加权Morrey空间上分数次极大算子的双权不等式

Ye与Wang研究了Hardy-Littlewood极算子在加权Morrey空间的双权不等式.该文将Ye与Wang的结果拓展到分数次极大算子,此外也得到了Ap型的充分条件.     

On the Coifman type inequality for the oscillation of one-sided averages

In this paper we study the Coifman type estimate for an oscillation operator related to the one-sided discrete square function S⁺. We prove that for any weight w, the Lp(w)-norm of this operator, and therefore the Lp(w)-norm of S⁺, is dominated by a constant times the Lp(w)-norm of the one-sided Hardy-Littlewood maximal function iterated two times. For the kth commutator with a BMO function we show that k+2 iterates of the one-sided Hardy-Littlewood maximal function are sufficient.     

A characterization of some weighted inequalities for the vector-valued weighted maximal function

We give in this paper a necessary and sufficient condition of weighted weak and strong type norm inequalities for the vector-valued weighted maximal function.     

Two-weight norm inequalities for fractional maximal functions and fractional integral operators on weighted Morrey spaces

In this paper, we consider weighted norm inequalities for fractional maximal operators and fractional integral operators. For suitable weights, we prove the two-weight norm inequalities for both operators on weighted Morrey spaces.     

Equivalence of operator norm for Hardy-Littlewood maximal operators and their truncated operators on Morrey spaces

We will prove that for 1相似文献   

向量值极大积分交换子的加权估计

考虑了极大向量值交换子的加权有界性.分别得到了强型和弱型的加权模不等式,其中权函数是非负局部可积函数.     

Sharp maximal inequality for stochastic integrals

Let be a nonnegative supermartingale and be a predictable process with values in . Let denote the stochastic integral of with respect to . The paper contains the proof of the sharp inequality

where . A discrete-time version of this inequality is also established.

     

Sharp bounds for fractional one-sided operators

In this paper,we characterize the sharp boundedness of the one-sided fractional maximal function for one-weight and two-weight inequalities.Also a new two-weight testing condition for the one-sided fractional maximal function is introduced extending the work of Martín-Reyes and de la Torre.Improving some extrapolation result for the one-sided case,we get weak sharp bounded estimates for one-sided fractional maximal function and weak and strong sharp bounded estimates for one-sided fractional integral.     

On some sharp weighted norm inequalities

Given a weight ω, we consider the space which coincides with when ω∈A_p. Sharp weighted norm inequalities on for the Calderón-Zygmund and Littlewood-Paley operators are obtained in terms of the A_p characteristic of ω for any 1<p<∞.     

加权幂平均不等式的加强

对加权幂平均不等式的加强作了全面的研究，推广了一个加强的加权算术-几何不等式．     

Strong maximal operator and singular integral operators in weighted Morrey spaces on product domains

We introduce the Morrey spaces on product domains and extend the boundedness of strong maximal operator and singular integral operators on product domains to Morrey spaces.     

A note on operator norm inequalities

If P is a positive operator on a Hilbert space H whose range is dense, then a theorem of Foias, Ong, and Rosenthal says that: [(P)]^–1T[(P)]<-12 max {T, P^–1TP} for any bounded operator T on H, where is a continuous, concave, nonnegative, nondecreasing function on [0, P]. This inequality is extended to the class of normal operators with dense range to obtain the inequality [(N)]^–1T[(N)]<-12c² max {tT, N^–1TN} where is a complex valued function in a class of functions called vase-like, and c is a constant which is associated with by the definition of vase-like. As a corollary, it is shown that the reflexive lattice of operator ranges generated by the range NH of a normal operator N consists of the ranges of all operators of the form (N), where is vase-like. Similar results are obtained for scalar-type spectral operators on a Hilbert space.This author gratefully acknowledges the support of Central Michigan University in the form of a Research Professorship.     

Mixed means over balls and annuli and lower bounds for operator norms of maximal functions

In this paper we prove mixed-means inequalities for integral power means of an arbitrary real order, where one of the means is taken over the ball , centered at and of radius , δ>0. Therefrom we deduce the corresponding Hardy-type inequality, that is, the operator norm of the operator S_δ which averages over , introduced by Christ and Grafakos in Proc. Amer. Math. Soc. 123 (1995) 1687-1693. We also obtain the operator norm of the related limiting geometric mean operator, that is, Carleman or Levin-Cochran-Lee-type inequality. Moreover, we indicate analogous results for annuli and discuss estimations related to the Hardy-Littlewood and spherical maximal functions.     

A note on one-sided interval edge colorings of bipartite graphs

For a bipartite graph G with parts X and Y, an X-interval coloring is a proper edge coloring of G by integers such that the colors on the edges incident to any vertex in X form an interval. Denote by ${\chi }_{int}^{\prime }(G,X)$ the minimum k such that G has an X-interval coloring with k colors. Casselgren and Toft (2016) [12] asked whether there is a polynomial $P(\mathrm{\Delta })$ such that if G has maximum degree at most Δ, then ${\chi }_{int}^{\prime }(G,X)\le P(\mathrm{\Delta })$. In this short note, we answer this question in the affirmative; in fact, we prove that a cubic polynomial suffices. We also deduce some improved upper bounds on ${\chi }_{int}^{\prime }(G,X)$ for bipartite graphs with small maximum degree.     

A note on the weighted Hilbert's inequality

A finite Hilbert transformation associated with a polynomial is the analogue of a Hilbert transformation associated with an entire function which is a generalization of the classical Hilbert transformation. The weighted Hilbert inequality, which has applications in analytic number theory, is closely related to the finite Hilbert transformation associated with a polynomial. In this note, we study a relation between the finite Hilbert transformation and the weighted Hilbert's inequality. A question is posed about the finite Hilbert transformation, of which an affirmative answer implies the weighted Hilbert inequality.

     

对一个不等式的一点注记

讨论了不等式bx+y-ax+y/bx-ax≥x+y/x(ab)r/2及其逆成立或不成立的一切情形,其中x,y∈R x≠0 a,b＞0,a≠b.     

A Hilbert-type integral inequality on the fractal space

Based on the local fractional calculus, by using the methods of weight function, a Hilbert-type fractal integral inequality and its equivalent form are given. Their constant factors are proved being the best possible, and its applications are discussed briefly.