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
The Frobenius Problem for Generalized Repunit Numerical SemigroupsMediterranean Journal of Mathematics - Tập 20 - Trang 1-18 - 2022
Manuel B. Branco, Isabel Colaço, Ignacio Ojeda
In this paper, we introduce and study the numerical semigroups generated by
$$\{a_1, a_2, \ldots \} \subset {\mathbb {N}}$$
such that
$$a_1$$
is the repunit number in base
...... 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,
$$\begin{aligned} {\left\{ \begin{array}{ll} (-\Delta )^{s}u(x)- \lambda \frac{u(x)}{|x|^{2s}}=u(x)^{p-1}+\mu u(x)...... hiện toàn bộ
Sharp Hardy Inequalities in Star-shaped Domains with Double Singular KernelsMediterranean Journal of Mathematics - Tập 14 - Trang 1-13 - 2016
Alexander Fabricant, Nikolai Kutev, Tsviatko Rangelov
Improved Hardy inequality with double singular kernel in bounded, star-shaped domains
$$\Omega \subset R^n$$
is proved. The case of singularity at an interior point and on the boundary of the domain is considered. The Hardy constant is optimal an...... hiện toàn bộ