Analysis and Mathematical Physics最新文献

In the present paper we deal with (local) infinitesimal isometries of special sub-Riemannian manifolds (a contact and oriented sub-Riemannian manifold is called special if the Reeb vector field is an infinitesimal isometry). The objective of the paper is to find some conditions on such manifolds which allow one to construct, locally around a given point, infinitesimal isometries and then, if possible, to prolong them onto bigger domains. The mentioned conditions are related to the so-called (mathfrak {i}^*)-regular and (mathfrak {i})-regular points, the notions introduced by Nomizu (Ann Math 2:105–120, 1960) in the Riemannian setting and slightly modified by the author.

The aim of this paper is to study the maximal commutators (M_{b}) and the commutators of the maximal operator [b, M] in the total Morrey spaces (L^{p,lambda ,mu }(mathbb {G})) on any stratified Lie group (mathbb {G}) when b belongs to Lipschitz spaces ({dot{Lambda }}_{beta }(mathbb {G})). Some new characterizations for certain subclasses of Lipschitz spaces ({dot{Lambda }}_{beta }(mathbb {G})) are given.

In this paper we obtain necessary and sufficient conditions for the boundedness in weighted Lebesgue spaces of one-dimensional Hardy-type operators involving suprema. In particular, we solve the problems from Frank RL (J. Math. Sci. 263:323-342, 2022)

In this paper we study special properties of solutions of the initial value problem associated to a class of nonlinear dispersive equations where the operator modelling dispersive effects is nonlocal. In particular, we prove that solutions of the surface tension Whitham equations posed on the real line satisfy the propagation of regularity phenomena, which says that regularity of the initial data on the right hand side of the real line is propagated to the left hand side by the flow solution. A similar result is obtained for solutions of the Full Dispersion Kadomtsev–Petviashvili equation, a natural (weakly transverse) two-dimensional version of the Whitham equation, with and without surface tension. We establish that the augmented regularity of the initial data on certain distinguished subsets of the Euclidean space is transmitted by the flow solution at an infinite rate. The underlying approach involves treating the general equation as a perturbed version of a class of fractional equations with well-established properties.

Let (Kge 1). We prove Zygmund theorem for (K-)quasiregular harmonic mappings in the unit disk (mathbb {D}) in the complex plane by providing a constant C(K) in the inequality

provided that (textrm{Im},f(0)=0). Moreover for a quasiregular harmonic mapping (f=(f_1,dots , f_n)) defined in the unit ball (mathbb {B}subset mathbb {R}^n), we prove the asymptotically sharp inequality

when (Krightarrow 1), provided that (f_1) is positive.

This paper is devoted to studying the boundedness of commutators (textrm{H}_{Omega ,beta }^b) generated by the rough fractional Hardy operators (textrm{H}_{Omega ,beta }) with the symbol b on the mixed radial-angular spaces. When b is a mixed radial-angular central bounded mean oscillation function and (Omega in L^s(S^{n-1})) for some (s>1), the boundedness of (textrm{H}_{Omega ,beta }^b) on the mixed radial-angular homogeneous Herz spaces is established. Meanwhile, the boundedness for (textrm{H}_{Omega ,beta }^b) on the mixed radial-angular homogeneous (lambda )-central Morrey spaces is also obtained, provided that b belongs to the mixed radial-angular homogeneous (lambda )-central bounded mean oscillation spaces and (Omega in L^s(S^{n-1})) for some (s>1).

This paper is divided into two parts. First, we will prove the existence of solutions of the p-Laplacian equation in the Riemannian manifold in the space ({mathcal {H}}^{alpha ,p}_{loc}({mathcal {N}})). On the other hand, we will give a criterion to obtain a positive lower bound for (lambda _{1,p}(Omega )), where is a bounded domain (Omega subset {mathcal {N}}). In the first result, we do not consider a bounded subset on the Riemannian manifold ({mathcal {N}}).

We present an extensive study on the Bergman kernel expansions and the random zeros associated with the high tensor powers of a semipositive line bundle on a complete punctured Riemann surface. We prove several results for the zeros of Gaussian holomorphic sections in the semi-classical limit, including the equidistribution, large deviation estimates, central limit theorem, and number variances.

The paper deals with the asymptotic properties of semigroups associated with Markov jump processes in a high contrast periodic medium in (mathbb {R}^d), (dge 1). In order to study the limit behaviour of these semigroups we equip the corresponding Markov processes with an extra variable that characterizes the position of the process inside the period, and show that the limit dynamics of these two-component processes remains Markov. We describe the limit process and prove the convergence of the corresponding semigroups as well as the convergence in law of the extended processes in the path space. Since the components of the limit process are coupled, the dynamics of the first (spacial) component need not have a semigroup property. We derive the evolution equation with a memory term for the dynamics of this component of the limit process. We also discuss the construction of the limit semigroup in the (L^2) space and study the spectrum of its generator.