Analysis and Mathematical Physics最新文献

In this paper necessary and sufficient conditions on a measure (mu ) guaranteeing the boundedness of the multilinear fractional integral operator (T_{gamma , mu }^{(m)}) (defined with respect to a measure (mu )) from the product of Lorentz spaces (prod _{k=1}^m L^{r_k, s_k}_{mu }) to the Lorentz space (L^{p,q}_{mu }(X)) are established. The results are new even for linear fractional integrals (T_{gamma , mu }) (i.e., for (m=1)). From the general results we have a criterion for the validity of Sobolev–type inequality in Lorentz spaces defined for non-doubling measures. Finally, we investigate the same problem for Morrey-Lorentz spaces. To prove the main result we use the boundedness of the multilinear modifies maximal operator (widetilde{mathcal {M}}).

We study homogenization problem for non-autonomous parabolic equations of the form (partial _t u=L(t)u) with an integral convolution type operator L(t) that has a non-symmetric jump kernel which is periodic in spatial variables and in time. It is assumed that the space-time scaling of the environment is not diffusive. We show that asymptotically the spatial and temporal evolutions of the solutions are getting decoupled, and the homogenization result holds in a moving frame.

We study the spectral properties of a Schrödinger operator, in presence of a confining potential given by the distance squared from a fixed compact potential well. We prove continuity estimates on both the eigenvalues and the eigenstates, lower bounds on the ground state energy, regularity and integrability properties of eigenstates. We also get explicit decay estimates at infinity, by means of elementary nonlinear methods.

In this work, we will study the existence, uniqueness and exponential stability of almost periodic solutions to the parabolic-elliptic Keller-Segel system on a real hyperbolic manifold. We clarify the existence and uniqueness of such solutions of the linear equation by utilizing the dispersive and smoothing estimates of the heat semigroup. Thereafter, we use the fixed point arguments to investigate for the case of the semi-linear equation by utilizing the results of the linear case. Finally, we invoke the Gronwall’s inequality to point out the exponential stability.

The goal of this paper is to refine the known Morrey-compactness result of commutators generated by (textrm{VMO}) functions and singular integral operators using closed subspaces of Morrey spaces. It turns out that such commutators map Morrey spaces into a different layer; specifically, compact commutators map Morrey spaces to their tilde-closed subspaces.

The algorithm for inverting covariant exterior derivative is provided. It works for a sufficiently small star-shaped region of a fibered set - a local subset of a vector bundle and associated vector bundle. The algorithm contains some constraints that can fail, giving no solution, which is the expected case for parallel transport equations. These constraints are straightforward to obtain in the proposed approach. The relation to operational calculus and operator theory is outlined. The upshot of this paper is to show, using the linear homotopy operator of the Poincare lemma, that we can solve the covariant constant and related equations in a geometric and algorithmic way. The considerations related to the regularity of the solutions are provided.

In this work, higher-order rogue wave solutions in the three-component local and nonlocal Gross-Pitaevskii equations are investigated. The first-order rogue wave solution for the three-component local and nonlocal Gross-Pitaevskii equations is derived using the Darboux transformation combined with a variable separation technique. In order to efficiently construct higher-order rogue wave solutions for the three-component local and nonlocal Gross-Pitaevskii equations, we establish a relationship between the three-component and the one-component versions of the nonlinear Schrödinger equation. Then using this relationship, we obtain the higher-order rational solutions for the three-component local and nonlocal Gross-Pitaevskii equations, which describe the rogue wave patterns. Moreover, the main characteristics of these rogue waves are graphically examined by varying the free parameters. In particular, these results show that rogue waves in the three-component nonlocal Gross-Pitaevskii equations may exhibit a much richer variety than those in the corresponding local equations.

In this paper, we define the concept of a cosmological time function on Lorentzian length spaces. We prove that a Lorentzian length space is globally hyperbolic if and only if the cosmological time function of a Lorentzian length space within its conformal class is regular. Additionally, we establish an ordering in the space of Lorentzian length spaces on a proper metric space and investigate stable causality in its fundamental form. Furthermore, we show that this definition of stable causality implies the existence of a time function inspired by the cosmological time function.

In this paper, we present new results on holomorphically accretive mappings and their resolvents defined on the open unit ball of a complex Banach space. We employ a unified approach to examine various properties of non-linear resolvents by applying a distortion theorem we have established. This method enables us to prove a covering result and to establish the accretivity of resolvents along with estimates of the squeezing ratio. Furthermore, we prove that under certain mild conditions, a non-linear resolvent is a starlike mapping of a specified order. As a key tool, we first introduce a refined version of the inverse function theorem for mappings satisfying so-called one-sided estimates.

Our first aim of this article is to establish several new versions of refined Bohr inequalities for bounded analytic functions in the unit disk involving Schwarz functions. Secondly, we obtain several new multidimensional analogues of the refined Bohr inequalities for bounded holomorphic mappings on the unit ball in a complex Banach space involving higher dimensional Schwarz mappings. All the results are proved to be sharp.