Related papers: Fractional series operators on $\mathbb{Z}^n$

We show, for a field ${\mathbb F}$ of prime characteristic $p>0$, that the truncated filiform Lie algebra ${\frak m}_0(p)$ admits a family ${\frak m}_0^\lambda(p)$ of restricted Lie algebra structures parameterized by elements $\lambda\in…

We obtain eigenvalues and eigenvectors of the $(\alpha,q)$-Bernstein operator $T_{n,q,\alpha}$. Moreover, we will give the limit behaviour of these eigenvalues and eigenvectors for all $q.$

Let $\,T^{j,k}_{N}:L^{p}(B)\, \rightarrow\,L^{q}([0,1])\,$ be the oscillatory integral operators defined by $\;\displaystyle T^{j,k}_{N}f(s):=\int_{B} \,f(x)\,e^{\imath N{|x|}^{j}s^{k}}\,dx, \quad (j,k)\in\{1,2\}^{2},\,$ where $\,B\,$ is…

In this paper, we introduce the variable Fofana's spaces $(L^{p(\cdot)},L^q)^\alpha (\mathbb{R}^n)$ where $1< p(\cdot)<\infty$ and $1\leq q,\alpha\leq\infty$, then show some properties and establish the pre-dual of those spaces which are…

In this paper, we prove that for $\frac{n}{2}+\frac{1}{4}<\alpha \leq\frac{n+1}{2} $, the convolution operator $$S_{\alpha} f(x)=\int_{|y| \geq 1} f(x-y)\left(|y|^{2}-1\right)^{-\alpha} d y$$ is bounded from $L^p$ to $L^q$ for certain…

This is a continuation of our previous research about an oscillatory integral operator $T_{\alpha, \beta}$ on compact manifolds $\mathbb{M}$. We prove the sharp $H^{p}$-$L^{p,\infty}$ boundedness on the maximal operator $T^{*}_{\alpha,…

The numerical range of a bounded linear operator on a complex Banach space need not be convex unlike that on a Hilbert space. The aim of this paper is to study operators $T$ on $ \ell^2_p $ for which the numerical range is convex. We also…

Let $f\colon\mathbb{N}\rightarrow\mathbb{N}_0$ be a multiplicative arithmetic function such that for all primes $p$ and positive integers $\alpha$, $f(p^{\alpha})<p^{\alpha}$ and $f(p)\vert f(p^{\alpha})$. Suppose also that any prime that…

In this paper we study integral operators with kernels \begin{equation*} K(x,y)= k_1( x- A_1y)...k_m( x-A_my), \end{equation*} $k_i(x)=\frac{\Omega_i(x)}{|x|^{n/q_i}}$ where $\Omega_i: \mathbb{R}^n\to \mathbb{R}$ are homogeneous functions…

Let $0<\alpha<n$ and $I_\alpha$ be the fractional integral operator. In this paper, we shall use a unified approach to show some boundedness properties of commutators $[b,I_\alpha]$ on the weighted Morrey spaces $L^{p,\kappa}(w)$ under…

We prove sharp weak type weighted estimates for a class of sparse operators that includes majorants of standard $\alpha$-fractional singular integrals, fractional integral operators, Marcinkiewicz integral operators, and square functions.…

This article investigates the Fourier extension operator associated with the fractional surface $(\xi,|\xi|^{\alpha})$ for $\alpha\geq 2$. We show that the relevant $L^p\to L^q$ Fourier extension inequality possesses extremals for all…

In this article, we propose new proportional fractional operators generated from local proportional derivatives of a function with respect to another function. We present some properties of these fractional operators which can be also…

In this paper we prove that an element $f\in \mathcal{A}(\mathbb{D})$ is a topological divisor of zero(TDZ) if and only if there exists $z_0 \in \mathbb{T}$ such that $f(z_0)=0.$ We also give a characterization of TDZ in the Banach algebra…

In this article, we show that multilinear fractional type operators are bounded from product Hardy spaces with variable exponents into Lebesgue spaces with variable exponents via the atomic decomposition theory. We also study continuity…

Let $\Delta^{(\alpha)}$ denote the fractional difference operator. In this paper, we define new difference sequence spaces $c_0(\Gamma,\Delta^{(\alpha)},u)$ and $c(\Gamma,\Delta^{(\alpha)},u)$. Also, the $\beta-$ dual of the spaces…

In this paper we investigate the $L^p$-boundedness of certain classes of periodic pseudo-differential operators. The operators considered arise from the study of symbols on $\mathbb{T}^n\times\mathbb{Z}^n$ with limited regularity.

Some mathematical models of applied problems lead to the need of solving boundary value problems with a fractional power of an elliptic operator. In a number of works, approximations of such a nonlocal operator are constructed on the basis…

We consider Fock spaces $F^{p,\ell}_{\alpha}$ of entire functions on ${\mathbb C}$ associated to the weights $e^{-\alpha |z|^{2\ell}}$, where $\alpha>0$ and $\ell$ is a positive integer. We compute explicitly the corresponding Bergman…

In this paper, we show the strong and weak type boundedness of $T_{\Omega,\alpha}^A$ and $M_{\Omega,\alpha}^A$, the multilinear fractional integral operators and the corresponding fractional maximal operators, on the two weights weighted…