Hölder and Minkowski type inequalities for pseudo-integral

There are proven generalizations of the Hölder’s and Minkowski’s inequalities for the pseudo-integral. There are considered two cases of the real semiring with pseudo-operations: one, when pseudo-operations are defined by monotone and continuous function g, the second semiring ([a, b], sup, ⊙), where ⊙ is generated and the third semiring where both pseudo-operations are idempotent, i.e., ⊕ = sup and ⊙ = inf.     

Hardy inequalities related to Grushin type operators

We prove some Hardy type inequalities related to the Grushin type operator .

     

The law of the iterated logarithm in game-theoretic probability with quadratic and stronger hedges

We prove both the validity and the sharpness of the law of the iterated logarithm in game-theoretic probability with quadratic and stronger hedges.     

Some new Gronwall-Bellman-Bihari type integral inequalities with delay

Some new linear and nonlinear delay integral inequalities of G-B-B type are obtained which generalize some results of O. Akinyele [1], P. Ch. Tsamatos and S. K. Ntouyas [16]. Application examples are also given. This revised version was published online in June 2006 with corrections to the Cover Date.     

Finsler Hardy inequalities

In this paper we present a unified simple approach to anisotropic Hardy inequalities in various settings. We consider Hardy inequalities which involve a Finsler distance from a point or from the boundary of a domain. The sharpness and the non-attainability of the constants in the inequalities are also proved.     

Mixed means and inequalities of Hardy and Levin-Cochran-Lee type for multidimensional balls

Integral means of arbitrary order, with power weights and their companion means, where the integrals are taken over balls in centered at the origin, are introduced and related mixed-means inequalities are derived. These relations are then used in obtaining Hardy and Levin-Cochran-Lee inequalities and their companion results for -dimensional balls. Finally, the best possible constants for these inequalities are obtained.

     

Some new inequalities involving the Hardy operator

In this paper we derive some new inequalities involving the Hardy operator, using some estimates of the Jensen functional, continuous form generalization of the Bellman inequality and a Banach space variant of it. Some results are generalized to the case of Banach lattices on $(0,b],0<b\le \infty$.     

General Hardy type inequality for seminormed fuzzy integrals

Hardy type inequality for seminormed fuzzy integrals based on an aggregation function is studied in a rather general form. The main results of this paper generalize some previous results. Also, some conclusions are drawn and some problems for further investigations are given.     

Berwald type inequality for Sugeno integral

Nonadditive measure is a generalization of additive probability measure. Sugeno integral is a useful tool in several theoretical and applied statistics which has been built on non-additive measure. Integral inequalities play important roles in classical probability and measure theory. The classical Berwald integral inequality is one of the famous inequalities. This inequality turns out to have interesting applications in information theory. In this paper, Berwald type inequality for the Sugeno integral based on a concave function is studied. Several examples are given to illustrate the validity of this inequality. Finally, a conclusion is drawn and a problem for further investigations is given.     

New general extensions of Chebyshev type inequalities for Sugeno integrals

We provide new frameworks of Chebyshev type inequalities for Sugeno integrals on abstract spaces.     

Bounds for Hardy type differences

Let A _k be an integral operator defined by

Marcinkiewicz积分交换子在一些Hardy空间的有界性

讨论了由核函数满足具有某类Dini条件的Marcinkiewicz积分μΩ及函数b∈Lipβ(R~n)生成的交换子μ(_Ω,b)~m的性质.证明了Marcinkiewicz积分交换子μ_(_Ω,b)~m在Hardy型空间H_(bm,s)(R~n)上有界,也在Herz型Hardy空间H_(bm)K_p~(a_q)(R~n)上有界.     

Some Hardy Type Inequalities in R~n

Some Hardy type inequalities on the ball and its complementary set in the Euclidean space are established by using the Picone type identity and constructing suitable auxiliary functions.     

Weighted Hardy and Rellich type inequalities on Riemannian manifolds

In this paper we present new results on two‐weight Hardy, Hardy–Poincaré and Rellich type inequalities with remainder terms on a complete noncompact Riemannian Manifold M. The method we use is flexible enough to obtain more weighted Hardy type inequalities. Our results improve and include many previously known results as special cases.     

A Hilbert-type integral inequality whose kernel is a homogeneous form of degree −3

In this paper, by estimating the weight function, we give a new Hilbert-type integral inequality whose kernel is a homogeneous form of degree −3 with the best constant factor and the reverse form is considered.     

Hardy inequalities for fractional integrals on general domains

We prove a sharp Hardy inequality for fractional integrals for functions that are supported in a general domain. The constant is the same as the one for the half-space and hence our result settles a recent conjecture of Bogdan and Dyda.     

Jackson-type and Bernstein-type inequalities for multipliers on Herz-type Hardy spaces

We establish Jackson-type and Bernstein-type inequalities for multipliers on Herz-type Hardy spaces. These inequalities can be applied to some important operators in Fourier analysis, such as the Bochner-Riesz multiplier over the critical index, the generalized Bochner-Riesz mean and the generalized Able-Poisson operator. This work was supported by Key Academic Discipline of Zhejiang Province of China and National Natural Science Foundation of China (Grant Nos. 10571014, 10631080, 10671019)