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Arash Ghorbanalizadeh

Publications and source records attributed to Arash Ghorbanalizadeh.

8 recordsLinked to original sources
arXiv2026

Density of Neural Network Classes on Compact Subsets of Topological Vector Spaces

We prove density results for neural-network classes on compact sets \(K\subset X\), where \(X\) is a topological vector space whose continuous dual \(X^*\) separates points. Let \(Ψ:\mathbb R\to\mathbb R\) be a continuous squashing function. We show that the class \[ Σ_X(Ψ) = \left\{ \sum_{j=1}^{N}ω_jΨ(f_j(x)+b_j): N\in\mathbb N,\ ω_j,b_j\in\mathbb R,\ f_j\in X^* \right\} \] is dense in \(C(K)\) with respect to the uniform norm. As a consequence, if \(μ\) is a Radon probability measure supported on \(K\), then \(Σ_X(Ψ)\) is dense in \(L^p(K,μ)\) for every \(1\le p<\infty\).

math.FA↗
arXiv2026

The Stein-Weiss inequality in variable exponent Morrey spaces

In this paper we prove the Stein-Weiss inequality in variable exponent Morrey spaces over a bounded domain. Our work extends earlier results in the variable exponent Lebesgue and Morrey settings, and utilizes new proof techniques applicable to Morrey spaces. We build on the foundational paper by Almeida, Hasanov, and Samko, which introduced Morrey spaces of variable exponents. As an application of our main result, we prove Poincaré-type inequalities using the approach of a recent paper by the first and third authors.

math.CA↗
arXiv2025

On Herz-Bochkarev limiting problem

This paper studies Hausdorff-Young-type inequalities within the framework of Lorentz spaces $L_{p,q}$. Focusing on the dependence of the associated constants on the integrability parameter $p$, we derive optimal bounds in the limiting case $p\rightarrow 2$, addressing the Herz-Bochkarev problem. The results obtained refine the pioneering estimates in [3] and are comparable to recent advances in [16]. The main ingredients of our approach are new grand Lorentz space techniques.

math.FA↗
arXiv2025

Discrete Hilbert Transform And Discrete Mikhlin Multiplier On Discrete Variable Lebesgue Space

In this paper, by using continuous Hilbert transform and maximal operator boundedness property in the variable Lebesgue space $ L^{p(\cdot)}(\mathbb{R}) $ we show that the discrete Hilbert transform is bounded in the variable discrete Lebesgue space $ \ell^{p_n}(\mathbb{Z}) $. We show that the discrete Mikhlin multiplier $ \mathcal{T}_m $ is a bounded operator on $ \ell^{p_n}(\mathbb{Z}) $ when $ 1<\underline{p}_n<\bar{p}_n<\infty $.

math.FA↗
arXiv2024

Some Remarks on the Vector-Valued Variable Exponent Lebesgue Spaces $\ell^{q(\cdot)} (L^{p(\cdot)})$

In this paper, we investigate the geometric properties of the variable mixed Lebesgue-sequence space $\ell^{q(\cdot)} (L^{p(\cdot)})$ as a Banach space. We show that, if $ 1<q_-,p_-,q_+,p_+<\infty $, then $\ell^{q(\cdot)} (L^{p(\cdot)})$ is strictly and uniformly convex. We also prove that when $ 1\le q_-,p_-,q_+,p_+<\infty, $ the convergence in norm implies the convergence in measure, and under some conditions on exponents, the approximation identity holds in the space $ \ell^1(L^{\frac{p(\cdot)}{q(\cdot)}}) $.

math.FA↗
arXiv2022

On the reflexivity of the spaces of variable integrability and summability

In this paper, we show that under the condition $ 1<p_-, q_-, p_+, q_+<\infty$, the space $\ell^{q(\cdot)} (L^{p(\cdot)})$ is reflexive. In this way we give an answer to open problem posed by Hästö in 2017 about the reflexivity of the variable mixed Lebesgue-sequence spaces $\ell^{q(\cdot)} (L^{p(\cdot)})$. What is important here is that the dual space of $\ell^{q(\cdot)} (L^{p(\cdot)})$ is specified. As its direct corollary, we show that the corresponding Besov space $B^{s(\cdot)}_{p(\cdot)q(\cdot)}$ is reflexive.

math.FA↗