Mediterranean Journal of Mathematics
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Some Notes on Endpoint Estimates for Pseudo-differential Operators
Mediterranean Journal of Mathematics - Tập 19 - Trang 1-14 - 2022
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 $$S^{m}_{\rho ,1}$$ or more generally in the rough Hörmander
class $$L^{\infty }S^{m}_{\rho }$$ with $$m\in \mathbb {R}$$ and $$\rho \in
[0,1]$$ . It i...
A-Spectral Permanence Property for $$C^*$$ -Algebras
Mediterranean Journal of Mathematics - Tập 21 - Trang 1-17 - 2024
For a positive element A of a $$C^*$$ -algebra $$\mathfrak {A}$$ , let $${\Vert
X\Vert }_{A}$$ denote the A-operator semi-norm of $$X\in \mathfrak {A}$$ . In
this paper, we aim to introduce and study the notion of A-spectrum for X, such
that $${\Vert X\Vert }_{A}<\infty $$ . In particular, when A is well supported,
we establish an A-spectral permanence property for $$C^*$$ -algebras....
The Frobenius Problem for Generalized Repunit Numerical Semigroups
Mediterranean Journal of Mathematics - Tập 20 - Trang 1-18 - 2022
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 $$b > 1$$ of length $$n > 1$$ and $$a_i - a_{i-1} = a\,
b^{i-2},$$ for every $$i \ge 2$$ , where a is a positive integer relatively
prime with $$a_1$$ . These numerical semigroups generalize the repunit numerical
semigroups amon...
Existence of Solutions for an Infinite System of Quadratic Integral Equations in the Banach Algebra $$C(I,c_0)$$
Mediterranean Journal of Mathematics - Tập 17 Số 1 - 2020
Cận trên và cận dưới thời gian bùng nổ đối với phương trình sóng loại Kirchhoff có độ damp mạnh với điều kiện hồi tưởng và phân rã phi tuyến Dịch bởi AI
Mediterranean Journal of Mathematics - Tập 15 - Trang 1-16 - 2018
Trong bài báo này, chúng tôi xem xét một phương trình sóng loại Kirchhoff có
dạng $$\begin{aligned}&u_{tt}-M(\Vert \nabla u\Vert _{2}^{2})\Delta u + \int
_{0}^{t}g(t-s)\Delta u(s)\mathrm{d}s+h(u_{t})-\mu \Delta u_{t}\\&\quad
=|u|^{\alpha }u,\quad \mathrm {trong}\quad \Omega \times (0,+\infty )
\end{aligned}$$. Dưới những giả thiết thích hợp về hạng mục dẻo và dữ liệu ban
đầu, chúng tôi chứng minh ...
#phương trình sóng #bùng nổ #loại Kirchhoff #điều kiện hồi tưởng #phân rã phi tuyến
Triviality and Rigidity of Almost Riemann Solitons
Mediterranean Journal of Mathematics - - 2024
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...
Existence of Solutions to Fractional Elliptic Equation with the Hardy Potential and Concave–Convex Nonlinearities
Mediterranean Journal of Mathematics - Tập 20 - Trang 1-16 - 2022
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,
$$\begin{aligned} {\left\{ \begin{array}{ll} (-\Delta )^{s}u(x)- \lambda
\frac{u(x)}{|x|^{2s}}=u(x)^{p-1}+\mu u(x)^{q-1}, &{}{} x\in \Omega ,\\
~~~~~~~~~~~~~~~~~~~~~~~~~u(x)>0, &{}{}x\...
Sharp Hardy Inequalities in Star-shaped Domains with Double Singular Kernels
Mediterranean Journal of Mathematics - Tập 14 - Trang 1-13 - 2016
Improved Hardy inequality with double singular kernel in bounded, star-shaped
domains $$\Omega \subset R^n$$ is proved. The case of singularity at an interior
point and on the boundary of the domain is considered. The Hardy constant is
optimal and the inequality is sharp due to the additional term....
The Multipoint Initial–Final Value Condition for the Hoff Equations on Geometrical Graph in Spaces of $$\mathbf{K}$$ -“noises”
Mediterranean Journal of Mathematics - Tập 19 - Trang 1-19 - 2022
We consider a linear stochastic Sobolev type equation with relatively p-bounded
operator and formulate a multipoint initial–final value condition for the
equation. In addition, we prove a theorem on the existence of a unique solution
to this problem in the space of $$\mathbf{K}$$ -“noises”. Abstract results are
used to study a specific multipoint initial–final value problem for linear
stochastic H...
Commutators of Some Maximal Functions with Lipschitz Function on Orlicz Spaces
Mediterranean Journal of Mathematics - Tập 15 - Trang 1-13 - 2018
Let $$0\le \alpha...
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