For a fixed nonnegative integer $m$, an analytic map $\varphi$ and function $\psi$, the generalized integration operator $I^{(m)}_{\varphi,\psi}$ is defined by \[ I^{(m)}_{\varphi,\psi} f(z) = \int_0^z f^{(m)}(\varphi(\zeta)) \psi(\zeta) \, d\zeta \] for $X$-valued $f$, where $X$ Banach space. Some estimates norm of $I^{(m)}_{\varphi,\psi} \colon wA^p_{\alpha}(X) \to A^p_{\alpha}(X)$ are obtain...

Abstract In this paper, we will study the Hardy and BMO spaces associated to generalized operator $$L_{\alpha }= (-\Delta )^{\alpha /2}+a|x|^{-\alpha }$$ L α = ( - Δ ) </mml:m...

Abstract In this paper we first establish the existence, uniqueness and Hölder continuity of solution to stochastic Volterra integral equations (SVIEs) with weakly singular kernels, singularities $\alpha \in (0, 1)$ for drift term $\beta 1/2)$ term. Subsequently, propose a $\theta $-Euler–Maruyama scheme Milstein solve numerically obtain strong rates convergence both schemes in $L^{p}$ norm any...

We study approximation properties of weighted $\mathrm{L}^2$-orthogonal projectors onto spaces polynomials bounded degree in the Euclidean unit ball, where weight is reflection-invariant form $(1-\lVert x \rVert^2)^\alpha \prod_{i=1}^d \lvert x_i \rvert^{\gamma_i}$, $\alpha, \gamma_1, \dots, \gamma_d > -1$. Said are measured Dunkl-Sobolev-type norms which same $\mathrm{L}^2$ norm used to contro...

concern over the depletion of natural resources in general, and water scarcity in particular, has stimulated the development and implementation of some policies aimed at changing farmers&apos; behavior in terms of conserving water. in this regard, government has recently begun to invest on researches supporting the technical solutions on conserving water in the agricultural sector as the bigges...

We show that the \(\alpha\)-fractional bilinear indicator/cube testing constant \(\mathcal{BICT}_{T^{\alpha }}\left( \sigma ,\omega \right) \equiv \sup_{Q\in \mathcal{P}^{n}}\sup_{E,F\subset Q}\frac{1}{\sqrt{\left\vert Q\right\vert_{\sigma }\left\vert Q\right\vert _{\omega }}}\left\vert \int_{F}T_{\sigma}^{\alpha }\left( \mathbf{1}_{E}\right) \omega \right\vert ,\) defined for any singular in...

We consider the Fr\"ohlich Hamiltonian with large coupling constant $\alpha$. For initial data of Pekar product form coherent phonon field and electron minimizing corresponding energy, we provide a norm approximation evolution, valid up to times order $\alpha^2$. The is given in terms state, evolved through Landau-Pekar equations, corrected by Bogoliubov dynamics taking quantum fluctuations int...

In this paper, we study the existence of normalized ground states to following lower critical fractional Choquard equation $ (-\Delta)^su = \lambda u+\gamma(I_{\alpha}*|u|^{1+\frac{\alpha}{N}})|u|^{\frac{\alpha}{N}-1}u+\mu |u|^{q-2}u\ \mbox{in}\ \mathbb R^N under L^2 $-norm constraint$ \int_{\mathbb R^N}|u|^2dx a^2, $where N \geq3 $, s\in(0,1) \alpha\in (0,N) a, \gamma, \mu&gt;0 and 2&lt;q\leq ...

‎In the present investigation‎, ‎we give the best estimates for the norm of the pre-Schwarzian derivative $ T_{f}(z)=dfrac{f^{''}(z)}{f^{'}(z)} $ for bi-starlike functions and a new subclass of bi-univalent functions of order $ alpha $‎, ‎where‎ ‎$Vert T_{f} Vert= sup_{|z|

In this paper we introduce and study Besselian $g$-frames. We show that the kernel of associated synthesis operator for a Besselian $g$-frame is finite dimensional. We also introduce $alpha$-dual of a $g$-frame and we get some results when we use the Hilbert-Schmidt norm for the members of a $g$-frame in a finite dimensional Hilbert space.