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1.
Wang  S.-Z.  Wang  Z.-H. 《Analysis Mathematica》2022,48(1):185-198
Analysis Mathematica - We investigate the relative operator entropies in the more general settings of C*-algebras, real C*-algebras and JC-algebras. We show that all the operator inequalities on...  相似文献   

2.
Nikoufar  Ismail  Fazlolahi  Maryam 《Positivity》2020,24(5):1503-1518
Positivity - The relative operator entropy has properties like operator means. In addition, the relative operator entropy has entropy-like properties. In this paper, we prove a Loewner–Heinz...  相似文献   

3.
An inequality of Hardy type is established for quadratic forms involving Dirac operator and a weight r b for functions in \mathbbRn{\mathbb{R}^n}. The exact Hardy constant c b  = c b (n) is found and generalized minimizers are given. The constant c b vanishes on a countable set of b, which extends the known case n = 2, b = 0 which corresponds to the trivial Hardy inequality in \mathbbR2{\mathbb{R}^2}. Analogous inequalities are proved in the case c b  = 0 under constraints and, with error terms, for a bounded domain.  相似文献   

4.
In our recent paper, we introduced the notions of relative operator (α,β)(α,β)-entropy and Tsallis relative operator (α,β)(α,β)-entropy as a parameter extensions of relative operator entropy and Tsallis relative operator entropy. In this paper, we give upper and lower bounds of these new notions according to operator (α,β)(α,β)-geometric mean introduced in Nikoufar et al. (2013) [14].  相似文献   

5.
In this article we produce Opial-type weighted multidimensional inequalities over balls and arbitrary smooth bounded domains. The inequalities are sharp. The functions under consideration vanish on the boundary.  相似文献   

6.
In this paper, we give a weighted form of the Hermite-Hadamard inequalities. Some applications of them are also derived. The results presented here would provide extensions of those given in earlier works. Finally we pose two interesting problems.  相似文献   

7.
8.
The generalized weighted mean operator ${\mathbf{M}^{g}_{w}}$ is given by $$[\mathbf{M}^{g}_{w}f](x) = g^{-1} \left( \frac{1}{W(x)} \int \limits_{0}^{x}w(t)g(f(t))\,{\rm d}t \right),$$ with $$W(x) = \int \limits_{0}^{x} w(s) {\rm d}s, \quad {\rm for} \, x \in (0, + \infty),$$ where w is a positive measurable function on (0, + ∞) and g is a real continuous strictly monotone function with its inverse g ?1. We give some sufficient conditions on weights u, v on (0, + ∞) for which there exists a positive constant C such that the weighted strong type (p, q) inequality $$\left( \int \limits_{0}^{\infty} u(x) \Bigl( [\mathbf{M}^{g}_{w}f](x) \Bigr)^{q} {\rm d}x \right)^{1 \over q} \leq C \left( \int \limits_{0}^{\infty}v(x)f(x)^{p} {\rm d}x \right)^{1 \over p}$$ holds for every measurable non-negative function f, where the positive reals p,q satisfy certain restrictions.  相似文献   

9.
In this paper the inequality
$$\begin{aligned} \bigg ( \int _0^{\infty } \bigg ( \int _x^{\infty } \bigg ( \int _t^{\infty } h \bigg )^q w(t)\,dt \bigg )^{r / q} u(x)\,{ ds} \bigg )^{1/r}\le C \,\int _0^{\infty } h v, \quad h \in {\mathfrak {M}}^+(0,\infty ) \end{aligned}$$
is characterized. Here \(0< q ,\, r < \infty \) and \(u,\,v,\,w\) are weight functions on \((0,\infty )\).
  相似文献   

10.
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.  相似文献   

11.
Harnack type inequalities for nonnegative (weak) solutions of degenerate elliptic equations, in divergence form, are established. The asymptotic behavior of solutions of Fuchsian type weighted elliptic operators is also investigated.  相似文献   

12.
In this work, we establish certain equivalences between the localisation properties with respect to spherical Fourier means of the support of a given Borel measure and the L 2-rate of decay of the Fourier extension operator associated to it. This, in turn, is intimately connected with the property that the X-ray transform of the measure be uniformly bounded. Geometric properties of sets supporting such a measure are studied. The research of this paper has been partially supported by the EU Comission via the network HARP, and by MEC Grant MTM2004-00678. The first author was partially supported by a Leverhulme Study Abroad Fellowship.  相似文献   

13.
Given a weight ω, we consider the space which coincides with when ωAp. Sharp weighted norm inequalities on for the Calderón-Zygmund and Littlewood-Paley operators are obtained in terms of the Ap characteristic of ω for any 1<p<∞.  相似文献   

14.
15.
A characterization of weighted Hardy inequalities in mixed norms on a half-axis is obtained.  相似文献   

16.
17.
In this paper, both the local and global weighted Sobolev-Poincaré imbedding inequalities and Poincaré inequalities for the composition T°G are established, where T is the homotopy operator and G is Green's operator applied to A-harmonic forms on manifolds.  相似文献   

18.
本文研究光滑度量测度空间上带权Paneitz算子的闭特征值问题和带权圆盘振动问题,给出Euclid空间、单位球面、射影空间和一般Riemann流形的n维紧子流形的权重Paneitz箅子和带权圆盘振动问题的前n个特征值上界估计.进一步地,本文给出带权Ricci曲率有界的紧致度量测度空间上带权圆盘振动问题的第一特征值的下界...  相似文献   

19.
The fractional maximal operator on homogeneous space (X, d, μ) is de fined as   相似文献   

20.
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.  相似文献   

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