arXiv subjects
Publications and source records attributed to Mitsuo Izuki.
The goal of this paper is to characterize the boundedness property of the uncentered Hardy--Littlewood maximal operator on ball Banach function spaces and their K\"{o}the associate spaces in terms of the vector-valued maximal inequality. The main result of this paper supplements the recent results by Nieraeth.
We establish a reproducing formula for the ridgelet transform on $\mathbb{R}^n$ in the framework of Banach lattices introduced in a recent paper by Nieraeth. Our approach is based on the $k$-plane Radon transform and a wavelet-type reconstruction operator acting on functions defined on the Grassmannian of $k$-dimensional affine planes. Under mild structural assumptions on the underlying Banach lattice, we prove that the ridgelet reconstruction converges both in the lattice norm and almost everywhere. The admissibility conditions on the wavelet function are formulated in terms of the Riemann--Liouville fractional integral. As a consequence, we obtain explicit inversion formulas for functions in a Banach lattice $X$ which is contained in $L^1({\mathbb R}^n)+L^p(\mathbb{R}^n)$ with some constant $1 \le p < \frac{n}{k}$, together with precise expressions for the reconstruction constant. These results provide a unified framework for ridgelet-type reproducing formulas in a broad class of function spaces beyond the classical $L^p$ setting.
In this paper, we extend several approximation theorems, originally formulated in the context of the standard $L^p$ norm, to the more general framework of variable exponent spaces. Our study is motivated by applications in neural networks, where function approximation plays a crucial role. In addition to these generalizations, we provide alternative proofs for certain well-known results concerning the universal approximation property. In particular, we highlight spaces with variable exponents as illustrative examples, demonstrating the broader applicability of our approach.
The aim of this paper is to apply an extrapolation result without relying on convexification. We characterize ball Banach function spaces in terms of wavelets, formulated in a way that takes into account the smoothness properties of the spaces under consideration. The same technique can also be applied to prove vector-valued inequalities, for example. Furthermore, the result presented here refines a recent extension operator result by Zhu, Yang, and Yuan.
This paper defines local weighted Hardy spaces with variable exponent. Local Hardy spaces permit atomic decomposition, which is one of the main themes in this paper. A consequence is that the atomic decomposition is obtained for the functions in the Lebesgue spaces with exponentially decaying exponent. As an application, we obtain the boundedness of singular integral operators, the Littlewood--Paley characterization and wavelet decomposition.
Our aim in this paper is to characterize local Muckenhoupt weighted Lebesgue spaces with variable exponent by compactly supported smooth wavelets. We also investigate necessary and sufficient conditions for the corresponding modular inequalities to hold. One big achievement is that the weights with exponetial growth can be handled in the framework of variable exponents.
Our aim is to study the modular inequalities for some operators, for example the Bergman projection acting on, in Lebesgue spaces with variable exponent. Under proper assumptions on the variable exponent, we prove that the modular inequalities are hold if and only if the exponent almost everywhere equals to a constant. In order to get the main results, we prove a lemma for a lower pointwise bound for these operators of a characteristic function.
We define new generalized Herz spaces having weight and variable exponent, that is, weighted Herz spaces with variable exponent. We prove the boundedness of an intrinsic square function on those spaces under proper assumptions on each exponent and weight.