Analysis and Mathematical Physics
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Global existence and blow-up for wave equation of p-Laplacian type
Analysis and Mathematical Physics - - 2023
This article explores a quasilinear wave equation of p-Laplacian type:
$$\begin{aligned} u_{tt}-\Delta _{p}u-\Delta u_t=|u|^{r-1}u \end{aligned}$$
in a bounded domain
$$\Omega \subset \mathbb {R}^{3}$$
......
On spectral asymptotic of quasi-exactly solvable quartic potential
Analysis and Mathematical Physics - - 2021
Motivated by the earlier results of Masoero and De Benedetti (Nonlinearity 23:2501, 2010) and Shapiro et al. (Commun Math Phys 311(2):277–300, 2012), we discuss below the asymptotic of the solvable part of the spectrum for the quasi-exactly solvable quartic oscillator. In particular, we formulate a conjecture on the coincidence of the asymptotic shape of the level crossings of the latter oscillato......
Necessary and sufficient conditions for the bounds of the commutator of a Littlewood-Paley operator with fractional differentiation
Analysis and Mathematical Physics - Tập 9 - Trang 2109-2132 - 2019
For $$b\in L_{\mathrm{loc}}({\mathbb {R}}^n)$$ and $$0<\alpha <1$$, we use fractional differentiation to define a new type of commutator of the Littlewood-Paley g-function operator, namely $$\begin{aligned} g_{\Omega ,\alpha ;b}(f )(x) =\bigg (\int _0^\infty \bigg |\frac{1}{t} \int _{|x-y|\le t}\frac{\Omega (x-y)}{|x-y|^{n+\alpha -1}}(b(x)-b(y))f(y)\,dy\bigg |^2\frac{dt}{t}\bigg )^{1/2}. \end{alig......
Initial boundary value problem for p-Laplacian type parabolic equation with singular potential and logarithmic nonlinearity
Analysis and Mathematical Physics - - 2023
The string equation for polynomials
Analysis and Mathematical Physics - Tập 8 Số 4 - Trang 637-653 - 2018
On sequences preserving q-Gevrey asymptotic expansions
Analysis and Mathematical Physics - - 2024
The modification of the coefficients of formal power series is analyzed in order that such variation preserves q-Gevrey asymptotic properties, in particular q-Gevrey asymptotic expansions. A characterization of such sequences is determined, providing a handy tool in practice. The sequence of q-factorials is proved to preserve q-Gevrey asymptotic expansions.
Variation type characterization of product Hardy spaces
Analysis and Mathematical Physics - - 2024
In the multidimensional Euclidean space, except the classical real Hardy space, there are numerous product ones. We associate with each of them a class of functions related to the known variations and new ones. Such a characterization is fulfilled by means of the integrability of the Fourier transform
Sharp pointwise gradient estimates for Riesz potentials with a bounded density
Analysis and Mathematical Physics - Tập 8 - Trang 711-730 - 2018
We establish sharp inequalities for the Riesz potential and its gradient in
$$\mathbb {R}^{n}$$
and indicate their usefulness for potential analysis, moment theory and other applications.
Hyponormal Toeplitz operators with non-harmonic algebraic symbol
Analysis and Mathematical Physics - Tập 9 - Trang 1613-1626 - 2019
Given a bounded function $$\varphi $$ on the unit disk in the complex plane, we consider the operator $$T_{\varphi }$$, defined on the Bergman space of the disk and given by $$T_{\varphi }(f)=P(\varphi f)$$, where P denotes the orthogonal projection to the Bergman space in $$L^2({\mathbb {D}},dA)$$. For algebraic symbols $$\varphi $$, we provide new necessary conditions on $$\varphi $$ for $$T_{\v......
Integrability conditions on a sub-Riemannian structure on $$\mathbb {S}^3$$
Analysis and Mathematical Physics - - 2017
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