Some Notes on Endpoint Estimates for Pseudo-differential OperatorsMediterranean Journal of Mathematics - Tập 19 - Trang 1-14 - 2022
Jingwei Guo, Xiangrong Zhu
We study the pseudo-differential operator
$$\begin{aligned} T_a f\left( x\right) =\int _{\mathbb {R}^n}e^{ix\cdot \xi }a\left( x,\xi \right) \widehat{f}\left( \xi \right) \,\text {d}\xi , \end{aligned}$$
where the symbol a is in the Hörmander class
...... hiện toàn bộ
Triviality and Rigidity of Almost Riemann SolitonsMediterranean Journal of Mathematics - - 2024
Amalendu Ghosh
In this paper, we study some triviality and rigidity results of Riemann soliton. First, we derive some sufficient conditions for which an almost Riemann soliton is trivial. In particular, we prove that any compact almost Riemann soliton with constant scalar curvature has constant sectional curvature. Next, we prove some rigidity results for gradient Riemann solitons. Precisely, we prove that a non...... hiện toàn bộ
Existence of Solutions to Fractional Elliptic Equation with the Hardy Potential and Concave–Convex NonlinearitiesMediterranean Journal of Mathematics - Tập 20 - Trang 1-16 - 2022
Xiangrui Li, Shuibo Huang, Qiaoyu Tian
In this paper, by a new variational principle established by Moameni, we establish the existence of solutions to the following fractional elliptic equation with the Hardy potential and concave–convex nonlinearities,
$$\begin{aligned} {\left\{ \begin{array}{ll} (-\Delta )^{s}u(x)- \lambda \frac{u(x)}{|x|^{2s}}=u(x)^{p-1}+\mu u(x)...... hiện toàn bộ
On Gradient Shrinking and Expanding Kähler–Ricci SolitonsMediterranean Journal of Mathematics - Tập 19 - Trang 1-12 - 2021
Liangdi Zhang
We prove that a compact gradient shrinking Kähler–Ricci soliton with subharmonic scalar curvature is Kähler–Einstein. Moreover, we show that a complete noncompact gradient shrinking Kähler–Ricci soliton with constant scalar curvature and nonnegative fourth-order divergence curvature (or Bochner) tensor is rigid. We also derive a classification theorem for complete noncompact gradient expanding Käh...... hiện toàn bộ
Aldo Cossu’s Work in Finite GeometryMediterranean Journal of Mathematics - Tập 3 - Trang 349-361 - 2006
Giorgio Faina, Gábor Korchmáros
A survey of the contributions of Aldo Cossu in finite geometry is given.
On Positive Solutions of Elliptic Equations with Oscillating Nonlinearity in $$\mathbb {R}^N$$Mediterranean Journal of Mathematics - Tập 19 - Trang 1-19 - 2022
Francisco J. S. A. Corrêa, Romildo N. de Lima, Alânnio B. Nóbrega
In this paper, we study results of existence and multiplicity of positive solutions for the following semilinear problem
$$\begin{aligned} \left\{ \begin{array}{lcl} -\Delta u= \lambda P(x)f(u)\, \text{ in } \, \mathbb {R}^N\\ \lim \limits _{|x|\rightarrow \infty }u(x)=0, \end{array} \right. \quad \quad \quad \quad \quad \quad \...... hiện toàn bộ
Christoffel Transforms and Hermitian Linear FunctionalsMediterranean Journal of Mathematics - Tập 2 - Trang 451-458 - 2005
Francisco Marcellán, Javier Hernández
In this contribution we are focused on some spectral transformations of Hermitian linear functionals. They are the analogues of the Christoffel transform for linear functionals, i. e. for Jacobi matrices which has been deeply studied in the past. We consider Hermitian linear functionals associated with a probability measure supported on the unit circle. In such a case we compare the Hessenberg mat...... hiện toàn bộ
Parseval Frames Built Up from Generalized Shift-Invariant SystemsMediterranean Journal of Mathematics - Tập 11 - Trang 617-632 - 2014
Sandra Saliani
Wavelet systems, and many of its generalizations such as wavelet packets, shearlets, and composite dilation wavelets are generalized shift-invariant systems (GSI) in the sense of the work by Ron and Shen. It is well known that a wavelet system is never Z-shift invariant (SI). Nevertheless, one can modify it and construct a Z-SI system, called a quasi-affine system, which shares most of the frame p...... hiện toàn bộ