Analysis Mathematica最新文献

We generalize a fundamental theorem on positive matrix semigroups stating that each component is either strictly positive for all times or identically zero (“Lévy’s Theorem”). Our proof of this fact that does not require the matrices to be continuous at time zero. We also provide a formulation of this theorem in the terminology of positive operator semigroups on sequence spaces.

Let (Omega) be a bounded domain in (mathbb{R}^n) with (nge2) and (sin(0,1)). Assume that (phi colon [0, infty) to [0, infty)) is a Young function obeying the doubling condition with the constant (K_phi< 2^{frac{n}{s}}). We demonstrate that (Omega) supports a ((phi_frac{n}{s}, phi))-Poincaré inequality if it is a John domain. Alternatively, assume further that (Omega) is a bounded domain that is quasiconformally equivalent to a uniform domain (for (ngeq3)) or a simply connected domain (for (n=2)), then we show that (Omega) is a John domain if a ((phi_frac{n}{s}, phi))-Poincaré inequality holds.

This paper presents two new geometric constants (mu(X,a)) and (mu'(X,a)),which extend the rectangular constants (mu(X)) and (mu'(X)). We firstly provide their bounds. Then the relationships between these geometric constants and the geometric properties of Banach spaces are discussed, including uniform nonsquareness, uniform convexity and uniform smoothness. Meanwhile, we provide several estimates of (mu(l_p,a)) and obtain some new upper bound estimates on (mu'(l_p,a)).

We present a proof of Maz'ya-Verbitsky capacitary inequalities in terms of Bessel potentials. It will be seen that the proof mainly relies on the localization techniques. Several types of Kerman-Sawyer conditions will be obtained throughout the proof as well.

In this paper we present time-dependent perturbations of second-order non-autonomous abstract Cauchy problems associated to a family of operators with constant domain. We make use of the equivalence to a first-order non-autonomous abstract Cauchy problem in a product space, which we elaborate in full detail. As an application we provide a perturbed non-autonomous wave equation.

Our goal in this paper is to establish some difference analogue of second main theorems for holomorphic curves into projective varieties intersecting arbitrary families of c-periodical hypersurfaces (fixed or moving) with truncated counting functions in various cases. Our results generalize and improve the previous results in this topic.

Let (mu_{M,D}) be the planar self-affine measure generated by an expanding integer matrix (Min M_2(mathbb{Z})) and an integer digit set (D={0,1,dots,q-1}v) with (vinmathbb{Z}^2setminus{0}), where (gcd(det(M),q)=1) and (qge 2) is an integer. If the characteristic polynomial of (M) is (f(x)=x^2+det(M)) and ({v, Mv}) is linearly independent, we show that there exist at most (q^2) mutually orthogonal exponential functions in (L^2(mu_{M,D})), and the number (q^2) is the best. In particular, we further give a complete description for the case (M= {rm diag}(s, t))with (gcd(st, q)=1). This extends the results of Wei and Zhang [24].

An RD-space (mathcal{X}) is a space of homogeneous type in the sense of Coifman and Weiss satisfying a certain reverse (volume) doubling condition.Let (L) be a non-negative self-adjoint operator acting on (L^2(mathcal{X})).Assume that (L) generates an analytic semigroup ({mathrm{e}^{-tL}}_{t>0}) whose kernels ({h_t(x,y)}_{t>0}) satisfy a generalized Gaussian heat kernel upper estimate.Roughly speaking, the heat kernel behavior is a mixture of locally Gaussian and sub-Gaussian at infinity.With the help of this Gaussian heat kernel, we first introduce a novel Morrey space and then prove that it coincides with the classical Morrey space.As applications, some new characterizations of square Morrey space are established via a Carleson measure condition.

We explore boundedness properties of some natural operators ofconvolution type in the context of metric measure spaces. Their study is suggested by certain transformations used in computer vision.

We deduce Dowker’s general ratio ergodic theorem, and a vari-ant of it, from the Chacon–Ornstein theorem.