Non-homogeneous Spaces Research Articles

PARKAGENT: An agent-based model of parking in the city

In this paper, we present PARKAGENT, an agent-based, spatially explicit model for parking in the city. Unlike traditional parking models, PARKAGENT simulates the behavior of each driver in a spatially explicit environment and is able to capture the complex self-organizing dynamics of a large collective of parking agents within a non-homogeneous (road) space. The model generates distributions of key values like search time, walking distance, and parking costs over different driver groups. It is developed as an ArcGIS application, and can work with a practically unlimited number of drivers. The advantages of the model are illustrated using a real-life case from Tel Aviv. Taking detailed data from field surveys, the model is used to study the impact of additional parking supply in a residential area with a shortage of parking places. The PARKAGENT model shows that additional parking supply linearly affects the occurrence of extreme values, but has only a weak impact on the average search time for a parking place or the average walking distance between the parking place and the destination.

Boundedness of Riesz Potentials in Nonhomogeneous Spaces

For a class of linear operators including Riesz potentials on ℝ d with a non-negative Radon measure μ, which only satisfies some growth condition, the authors prove that their boundedness in Lebesgue spaces is equivalent to their boundedness in the Hardy space or certain weak type endpoint estimates, respectively. As an application, the authors obtain several new end estimates.

On similarity homogeneous locally compact spaces with intrinsic metric

In this article, we generalize partially the theorem of V. N. Berestovskii on characterization of similarity homogeneous (nonhomogeneous) Riemannian manifolds, i.e., Riemannian manifolds admitting transitive group of metric similarities other than motions to the case of locally compact similarity homogeneous (nonhomogeneous) spaces with intrinsic metric satisfying the additional assumption that the canonically conformally equivalent homogeneous space is δ-homogeneous or a space of curvature bounded below in the sense of A. D. Aleksandrov. Under the same assumptions, we prove the conjecture of V. N. Berestovskii on topological structure of such spaces.

A Class of Commutators for Multilinear Fractional Integrals in Nonhomogeneous Spaces

Let be a nondoubling measure on . A class of commutators associated with multilinear fractional integrals and RBMO( ) functions are introduced and shown to be bounded on product of Lebesgue spaces with .

The Cauchy Problem of the Nonlinear Schrödinger Equations in ℝ1+1

In this paper, we consider the local and global solution for the nonlinear Schrodinger equation with data in the homogeneous and nonhomogeneous Besov space and the scattering result for small data. The techniques to be used are adapted from the Strichartz type estimate, Kato’s smoothing effect and the maximal function (in time) estimate for the free Schrodinger operator.

VECTOR VALUED COMMUTATORS ON NON-HOMOGENEOUS SPACES

Let $\mu$ be a Borel measure on $\mathbb{R}^d$ which may be non doubling. The only condition that $\mu$ must satisfy is $\mu(Q) \leq c_0 l(Q)^n$ for any cube $Q \subset \mathbb{R}^d$ with sides parallel to the coordinate axes and for some fixed $n$ with $0 \lt n \leq d$. This paper is to develop the vector valued commutator theory in the context of the non-thomogeneous spaces. As an application, the boundedness of the maximal commutator of any Calderón-Zygmund operator on the non-homogeneous space with a $RBMO(\mu)$ function introduced by Tolsa in [9] is obtained.

Boundedness of Commutators with Lipschitz Functions in Non-homogeneous Spaces*

Under the assumption that $\mu$ is a non-doubling measure on ${\Bbb R}^d$, the authors obtain the boundedness of commutators generated by Calder\'on-Zygmund operators or fractional integrals with Lipschitz functions in the Lebesgue space and the Hardy space.

Spectroscopy of PVK-phenyl derivatives disturbed the long-range ordering of liquid crystalline phase

It has been shown that replacing of O–CH3 substituents in PVK-phenyl derivative chromophores by C–N groups leads to appearance of long-ranged dipole–dipole interactions in the composites including PVK-CN, fullerenes and cyano-biphenyl derivatives. Following quantum chemical calculations it has been demonstrated that interaction of the chromophores with the LC matrices favors dipole–dipole ordering, however it description requires to take into account non-homogenous space charge density distribution. During doping by PVK-CN derivatives phase transition has been found from uniaxial system with pure nematic to the quasi-smectic LC state with the substantially different parameter of ordering. Moreover it was established that during this substitution the switching times drastically jump from millisecond to microsecond regime.

Limiting case of the boundedness of fractional integral operators on nonhomogeneous space

We show the boundedness of fractional integral operators by means of extrapolation. We also show that our result is sharp.

Weighted estimates for commutators on nonhomogeneous spaces

Let be a Borel measure on which may be nondoubling. The only condition that must satisfy is for any cube with sides parallel to the coordinate axes and for some fixed with . This paper is to establish the weighted norm inequality for commutators of Calderon-Zygmund operators with functions by an estimate for a variant of the sharp maximal function in the context of the nonhomogeneous spaces.

Outer measures and weak type (1,1) estimates of Hardy-Littlewood maximal operators

We will introduce the times modified centered and uncentered Hardy-Littlewood maximal operators on nonhomogeneous spaces for. We will prove that the times modified centered Hardy-Littlewood maximal operator is weak type bounded with constant when if the Radon measure of the space has "continuity" in some sense. In the proof, we will use the outer measure associated with the Radon measure. We will also prove other results of Hardy-Littlewood maximal operators on homogeneous spaces and on the real line by using outer measures.

On Some Weighted Inequalities for Fractional Integrals on Nonhomogeneous Spaces

On Some Weighted Inequalities for Fractional Integrals on Nonhomogeneous Spaces

Local hardy and BMO spaces on non-homogeneous spaces

AbstractLet µ be Radon measure on Rd which may be non doubling. The only condition that µ must satisfy is the size condition µ(B(x, r)) ≤ Crn for some fixed n є (0, d). Recently, Tolsa introduced the spaces RBMO(µ) and Hatb1.∞ (µ), which, in some ways, play the role of the classical spaces BMO and H1 in case u is a doubling measure. In this paper, the author considers the local versions of the spaces RBMO(µ) and Hatb1.∞ (µ) in the sense of Goldberg and establishes the connections between the spaces RBMO(µ) and Hatb1.∞ (µ) with their local versions. An interpolation result of linear operators is also given.

T1 theorem for Besov spaces on nonhomogeneous spaces

Suppose μ is a Radon measure on ℝd, which may be non doubling. The only condition assumed on μ is a growth condition, namely, there is a constant C0>0 such that for all x∈supp(μ) and r>0, μ(B(x, r))⪯C0rn, where 0<n⪯d. We prove T1 theorem for non doubling measures with weak kernel conditions. Our approach yields new results for kernels satisfying weakened regularity conditions, while recovering previously known Tolsa’s results. We also prove T1 theorem for Besov spaces on nonhomogeneous spaces with weak kernel conditions given in [7].

Weighted Estimates for Operators Generated by Maximal Functions on Nonhomogeneous Spaces

Abstract We consider weighted weak type estimates for the modified Hardy–Littlewood maximal functions on a nonhomogeneous space. We use the new covering lemma by Sawano.

The Tb-theorem on non-homogeneous spaces

0 Introduction: main objects and results 3 0.1 Main results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 0.2 An application of T1-heorem: electric intensity capacity . . . . . . . . . . . . 7 0.3 How to interpret Calderon–Zygmund operator T? . . . . . . . . . . . . . . . 9 0.3.1 Bilinear form is defined on Lipschitz functions . . . . . . . . . . . . . 10 0.3.2 Bilinear form is defined for smooth functions . . . . . . . . . . . . . . 11 0.3.3 Apriori boundedness . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 0.4 Plan of the paper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

A Theorem on Multiplicators in Nonhomogeneous Hölder Spaces and Some of Its Applications

In Sec. 2, sufficient conditions of the boundedness of convolution operators with kernel m in a nonhomogeneous Holder space are given in terms of the Fourier-image of m. After that, the results of Sec. 2 are used to prove the solvability in a Holder space of the Cauchy problem for linear systems of the hydrodynamic type. Bibliography: 6 titles.

NEW WAVELET BASES FOR NON-HOMOGENEOUS SYMBOLIC SPACE AND RELATED KERNEL-DISTRIBUTION SPACES

This paper constructs several classes of new wavelet bases, which are unconditional bases for related operator spaces. Using these bases, the author analyzes non-homogeneous symbolic space and two related kernel-distribution spaces, and characterizes them in two wavelet coefficients spaces. Besides, some properties for singular integral operators are studied.

Electrical impedance evaluation in a conductive–dielectric half space by the charge simulation method

Electrical impedance in a non-homogeneous half space is considered by the charge simulation method (CSM). The CSM is a kind of the direct boundary element method, which is suitable for the infinite exterior analysis, as it only requires the discretization over the boundary surfaces between the regions. The electrical grounding systems are modelled, in which some numerical solutions are demonstrated for the impedance evaluation at the electrode placed in the half space and the potential distribution is visualized.

Accretive system Tb-theorems on nonhomogeneous spaces

We prove that the existence of an accretive system in the sense of M. Christ is equivalent to the boundedness of a Calderon-Zygmund operator on L2(μ)$. We do not assume any kind of doubling condition on the measure $\mu$, so we are in the nonhomogeneous situation. Another interesting difference from the theorem of Christ is that we allow the operator to send the functions of our accretive system into the space bounded mean oscillation (BMO) rather than L\sp ∞. Thus we answer positively a question of Christ as to whether the L\sp ∞-assumption can be replaced by a BMO assumption. We believe that nonhomogeneous analysis is useful in many questions at the junction of analysis and geometry. In fact, it allows one to get rid of all superfluous regularity conditions for rectifiable sets. The nonhomogeneous accretive system theorem represents a flexible tool for dealing with Calderon-Zygmund operators with respect to very bad measures.