Regularity results for the gradient of solutions linear elliptic equations with L 1, λ data

We prove that if f belongs to the Morrey space , with λ ∊ [0, n−2], and u is the solution of the problem

Info-quantifiers’ map-characterization revisited

We highlight the potentiality of a special Information Theory (IT) approach in order to unravel the intricacies of nonlinear dynamics, the methodology being illustrated with reference to the logistic map. A rather surprising dynamic feature→plane-topography map becomes available.     

Riesz potential estimates for a class of double phase problems

A double phase problem with a bounded Borel measure on the right hand side is studied. We prove an optimal pointwise gradient estimate for such a measure data problem via Riesz potentials of the measure under log-Dini continuity assumption on the modulating coefficients. As a consequence, we find an optimized $C^1$ regularity criterion.     

齐型空间上的Morrey空间广义极大算子的有界性

主要讨论了齐型空间上的Morrey空间极大算子的有界性,得到了极大算子Mq与M的一个等价关系,即Mq是Lp,(Ф)(X,μ)到Lp,(Ф)(X ,β)有界的等价M的有界性.     

An Application of Calculus on Measure Chains to Fourier Theory and Heisenberg's Uncertainty Principle

We present "one-dimensional" Fourier theory on commutative groups T hH , 0 h h < X , 0< H h X within the framework of the so-called calculus on measure chains (or time scales). Depending on certain values of the graininess h and length H of the group the four classical types of Fourier transform are covered: Fourier integral ( T 0 X = R ), Fourier series ( T 1 X = Z ), Fourier analysis of periodic functions ( T 0,2 ~ = S 1 (0) unit circle) and discrete Fourier transform ( T 1 N = Z N ). We will present Fourier theory on these groups in a unified manner. This also allows to closely track the roles of the graininess h and length H of the group--especially for h M 0 and H M X . In the final part of the paper, we investigate the solution of a fundamental equation on T hH , which can be considered as a generalization of the Gauss function. It finally leads to a version of the Heisenberg uncertainty principle, which extends the classical one, valid for T 0 X = R , to the case T hH , where either h >0 or H < X .     

On First Order Impulsive Dynamic Equations on Time Scales

In this paper, the nonlinear alternative of Leray-Schauder type is used to investigate the existence of solutions for first order impulsive dynamic equations on time scales.     

On Boundary Conditions for Wedge Operators on Radial Sets

We present a theorem about calculation of fixed point index for k-ψ-contractive operators with 0 ≤ k < 1 defined on a radial set of a wedge of an infinite-dimensional Banach space. Then, results on the existence of eigenvectors and nonzero fixed points are obtained.     

Relationships Between Various Outer Measures Induced by Lattice Measures

In this paper, we work with lattice spaces. (A lattice space is an ordered pair consisting of a set X and a lattice on X). As is known, each lattice measure µ induces six outer measures on P(X), one of which is the well-known "induced outer measure" µ^*(in case µ is countably additive); the others are µ, µ, µ,, and .In the first part of the paper, we consider an arbitrary lattice measure and discover various relationships involving two or more of the seven set functions under consideration, on P(X) and on various special subsets of P(X), under various conditions on the measure or on the lattice.In the second part of the paper, we consider two lattice measures related by "domination" and obtain similar results.In the third part of the paper, we consider two lattice measures related by "restriction" and obtain similar results.     

Weakly o‐Minimal Expansions of Boolean Algebras

We propose a definition of weak o‐minimality for structures expanding a Boolean algebra. We study this notion, in particular we show that there exist weakly o‐minimal non o‐minimal examples in this setting.     

关于Lebesgue分解定理的证明

提供了Lebesgue分解定理的又一证明,由此可以简化Lebesgue积分基本定理的证明．这对现代分析学教程的简化和学习无疑是非常有益的。