Mathematische Nachrichten最新文献

The authors introduce generalized Campanato space with regularized condition over non-homogeneous space, and study its basic properties including the John–Nirenberg inequality and equivalent characterizations. As applications, the boundedness of fractional type Marcinkiewicz integral and its commutator on generalized Morrey space over non-homogeneous space is obtained.

A new family of Volterra-type operators $��V_{�\alpha �,�\beta �}^{\phi }��(�·�)��$ based on bona fide fractional calculus is introduced in [12] by constructing analytic paraproducts acting on $��H�\left(�D�\right)�$ and their boundedness between Hardy spaces is characterized for certain parameter ranges there. This paper is a natural companion to [12] in the sense that it characterizes those $�\phi$’s such that $�V_{�\alpha �,�\beta �}^{\phi }$ is bounded from weighted Bergman spaces $��L_a^p��\left(�d�A_{\gamma }�\right)��$ to Hardy spaces $�H^q$ for the range

In this paper, we study the Dirichlet series that enumerates proper equivalence classes of full-rank sublattices of a given quadratic lattice in a hyperbolic plane—that is, a nondegenerate isotropic quadratic space of dimension 2. We derive explicit formulas for the associated zeta functions and obtain a combinatorial way to compute them. Their analytic properties lead to the intriguing consequence that a large proportion of proper classes are one-lattice classes.

This paper deals with a two-species chemotaxis-competition system in a setting that not only accounts for a class of nonlinear variants of the chemotactic cross-diffusion processes, but also involves an external source describing a superlinear growth effect under nonlocal resource consumption. Apart from that, the considered chemoattractant is assumed to be produced according to a fairly general power law. We first confirm the global existence and boundedness of classical solutions to an associated Neumann initial-boundary value problem under some appropriate parameter conditions. Moreover, it is shown that these global bounded solutions converge to the spatially homogeneous coexistence state as time tends to infinity.

We discuss families of hypersurfaces with isolated singularities in projective space with the property that the sum of the ranks of the rational homotopy and the homology groups is finite. They represent infinitely many distinct homotopy types with all hypersurfaces having a nef canonical or anti-canonical class. In the Appendix, we show that such an infinite family of smooth rationally elliptic 3-folds does not exist.

In this paper, we study a higher-order Laplacian operator in the framework of Orlicz–Sobolev spaces, the biharmonic g-Laplacian

A degenerate wave equation with time-varying delay in the boundary control input is considered. The well-posedness of the system is established by applying the semigroup theory. The boundary stabilization of the degenerate wave equation is concerned and the uniform exponential decay of solutions is obtained by combining the energy estimates with suitable Lyapunov functionals and an integral inequality under suitable conditions.

We obtain an $��L^1�\to �L^p�$ estimate in weighted $�L^p$ norms for the $�\overline{\partial }$-equation in $�C^n$ under a coercivity condition of the associated weighted Kohn Laplacian.

We study continuity of the multiplier operator $�e^{�i�q�}$ acting on Gelfand–Shilov spaces, where $�q$ is a polynomial on $�R^d$ of degree at least two with real coefficients. In the parameter quadrant for the spaces, we identify a wedge that depends on the polynomial degree for which the operator is continuous. We also show that in a large part of the complement region the operator is not continuous in dimension one. The results give information on well-posedness for linear evolution equations that generalize the Schrödinger equation for the free particle.