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Hitoshi Tanaka

Publications and source records attributed to Hitoshi Tanaka.

At least 19 recordsLinked to original sources
arXiv2026

The Kerman-Sawyer trace theorem for product Morrey spaces

By using parallel corona decomposition, the Kerman-Sawyer trace theorem is extended from Lebesgue spaces to \textit{product Morrey spaces}. By discretizing the multilinear fractional integral operator based on dyadic analysis, the framework of \textit{product Morrey spaces} naturally arises in the course of estimating the operator. Within this natural setting, by establishing Sawyer-type testing estimates (to the setting of measures), we obtain an extension of the Kerman-Sawyer trace theorem. The classical approach to the Kerman-Sawyer trace theorem typically relies on a reduction to Carleson's embedding theorem. In contrast, in this paper we employ a parallel corona decomposition, which allows us to overcome the difficulties inherent in the multilinear setting and to provide a transparent and streamlined proof. By incorporating recent developments in the theory of weights, this work clarifies the relationship between trace inequalities and Morrey spaces and contributes to a deeper understanding of these topics.

math.FA↗
arXiv2026

Multilinear embedding theorem for fractional sparse operators

We show some simple sufficient conditions for which the multilinear embedding theorem holds for fractional sparse operators. By verifying these conditions, we establish the theorem for power weights. We also provide Morrey-type sufficient conditions for which the $L^p \to L^q$, $1<p,q<\infty$, infinitesimal relative bounds hold for Schr\"{o}dinger operators of the form $(-\Delta)^{\alpha/2}+v$.

math.FA↗
arXiv2024

Commissioning of a compact multibend achromat lattice: A new 3 GeV synchrotron radiation facility

NanoTerasu, a new 3 GeV synchrotron light source in Japan, began user operation in April 2024. It provides high-brilliance soft to tender X-rays and covers a wide spectral range from ultraviolet to tender X-rays. Its compact storage ring with a circumference of 349 m is based on a four-bend achromat lattice to provide two straight sections in each cell for insertion devices with a natural horizontal emittance of 1.14 nm rad, which is small enough for soft X-rays users. The NanoTerasu accelerator incorporates several innovative technologies, including a full-energy injector C-band linear accelerator with a length of 110 m, an in-vacuum off-axis injection system, a four-bend achromat with B-Q combined bending magnets, and a TM020 mode accelerating cavity with built-in higher-order-mode dampers in the storage ring. This paper presents the accelerator machine commissioning over a half-year period and our model-consistent ring optics correction. The first user operation with a stored beam current of 160 mA is also reported. We summarize the storage ring parameters obtained from the commissioning. This is helpful for estimating the effective optical properties of synchrotron radiation at NanoTerasu.

physics.acc-ph↗
arXiv2023

Choquet integrals, Hausdorff content and sparse operators

Let $H^d$, $0 0$. In this paper we verify that the sparse operator ${\mathcal A}_{{\mathcal S}}$ maps ${\mathcal L}^p(H^d)$, $1\le p<\infty$, into an associate space of Orlicz-Morrey space ${{\mathcal M}^{p'}_{\Phi_0}(H^d)}'$, $\Phi_0(t)=t\log(e+t)$. We also give another characterizations of those associate spaces using the tiling ${\mathcal T}$ of ${\mathbb R}^n$.

math.FA↗
arXiv2023

The rectangular fractional integral operators

With rectangular doubling weight, a~generalized Hardy-Littlewood-Sobolev inequality for rectangular fractional integral operators is verified. The result is a~nice application of $M$-linear embedding theorem for dyadic rectangles.

math.CA↗
arXiv2023

Choquet integrals, Hausdorff content and fractional operators

It is shown that the fractional integral operator $I_{\alpha}$, $0<\alpha<n$, and the fractional maximal operator $M_{\alpha}$, $0\le\alpha<n$, are bounded on weak Choquet spaces with respect to Hausdorff content. We also investigate these operators on Choquet-Morrey spaces. These results are extensions of the previous works due to Adams, Orobitg and Verdera, and Tang. The results for the fractional integral operator $I_{\alpha}$ are essentially new.

math.FA↗
arXiv2022

Deep Learning-enabled Detection and Classification of Bacterial Colonies using a Thin Film Transistor (TFT) Image Sensor

Early detection and identification of pathogenic bacteria such as Escherichia coli (E. coli) is an essential task for public health. The conventional culture-based methods for bacterial colony detection usually take >24 hours to get the final read-out. Here, we demonstrate a bacterial colony-forming-unit (CFU) detection system exploiting a thin-film-transistor (TFT)-based image sensor array that saves ~12 hours compared to the Environmental Protection Agency (EPA)-approved methods. To demonstrate the efficacy of this CFU detection system, a lensfree imaging modality was built using the TFT image sensor with a sample field-of-view of ~10 cm^2. Time-lapse images of bacterial colonies cultured on chromogenic agar plates were automatically collected at 5-minute intervals. Two deep neural networks were used to detect and count the growing colonies and identify their species. When blindly tested with 265 colonies of E. coli and other coliform bacteria (i.e., Citrobacter and Klebsiella pneumoniae), our system reached an average CFU detection rate of 97.3% at 9 hours of incubation and an average recovery rate of 91.6% at ~12 hours. This TFT-based sensor can be applied to various microbiological detection methods. Due to the large scalability, ultra-large field-of-view, and low cost of the TFT-based image sensors, this platform can be integrated with each agar plate to be tested and disposed of after the automated CFU count. The imaging field-of-view of this platform can be cost-effectively increased to >100 cm^2 to provide a massive throughput for CFU detection using, e.g., roll-to-roll manufacturing of TFTs as used in the flexible display industry.

physics.ins-det↗
arXiv2020

A Forced Harmonic Oscillator, Interpreted as Diffraction of Light

We investigate a simple forced harmonic oscillator with a natural frequency varying with time. It is shown that the time evolution of such a system can be written in a simplified form with Fresnel integrals, as long as the variation of the natural frequency is sufficiently slow compared to the time period of oscillation. Thanks to such a simple formulation, we found, for the first time, that a forced harmonic oscillator with a slowly-varying natural frequency is essentially equivalent to diffraction of light.

physics.class-ph↗
arXiv2017

Tsunami Bores in Kitakami River

The 2011 Tohoku tsunami entered the Kitakami river and propagated there as a train of shock waves, recorded with a 1-min interval at water level stations at Fukuchi, Iino, and the weir 17.2 km from the mouth, where the bulk of the wave was reflected back. The records showed that each bore kept its shape and identity as it traveled a 10.9-km-path Fukuchi-Iino-weir-Iino. Shock handling based on the cross-river integrated classical shock conditions was applied to reconstruct the flow velocity time histories at the measurement sites, to estimate inflow into the river at each site, to evaluate the wave heights of incident and reflected tsunami bores near the weir, and to estimate propagation speed of the individual bores. Theoretical predictions are verified against the measurements. We discuss experiences of exercising the shock conditions with actual tsunami measurements in the Kitakami river, and test applicability of the shallow-water approximation for describing tsunami bores with heights ranging from 0.3 m to 4 m in a river segment with a depth of 3-4 m.

physics.ao-ph↗
arXiv2017

The $n$-linear embedding theorem for dyadic rectangles

Let $\sg_i$, $i=1,\ldots,n$, denote reverse doubling weights on $\R^d$, let $\cdr(\R^d)$ denote the set of all dyadic rectangles on $\R^d$ (Cartesian products of usual dyadic intervals) and let $K:\,\cdr(\R^d)\to[0,\8)$ be a~map. In this paper we give the $n$-linear embedding theorem for dyadic rectangles. That is, we prove the $n$-linear embedding inequality for dyadic rectangles \[ \sum_{R\in\cdr(\R^d)} K(R)\prod_{i=1}^n\lt|\int_{R}f_i\,{\rm d}\sg_i\rt| \le C \prod_{i=1}^n \|f_i\|_{L^{p_i}(\sg_i)} \] can be characterized by simple testing condition \[ K(R)\prod_{i=1}^n\sg_i(R) \le C \prod_{i=1}^n\sg_i(R)^{\frac{1}{p_i}} \quad R\in\cdr(\R^d), \] in the range $1 1$. As a~corollary to this theorem, for reverse doubling weights, we verify a~necessary and sufficient condition for which the weighted norm inequality for the multilinear strong positive dyadic operator and for strong fractional integral operator to hold.

math.FA↗
arXiv2017

Fractional maximal operators with weighted Hausdorff content

Let $n\ge 2$ be the spatial dimension. The purpose of this note is to obtain some weighted estimates for the fractional maximal operator ${\mathfrak M}{\alpha}$ of order $\alpha$, $0\le\alpha<n$, on the weighted Choquet-Lorentz space $L^{p,q}(H_{w}^{d})$, where the weight $w$ is arbitrary and the underlying measure is the weighted $d$-dimensional Hausdorff content $H^{d}_{w}$, $0<d\le n$. Concerning a dependence of two parameters $\alpha$ and $d$, we establish a general form of the Fefferman-Stein type inequalities for ${\mathfrak M}_{\alpha}$. Our results contain the works of Adams, \cite{Ad} and of Orobitg and Verdera \cite{OV} as the special cases. Our results also imply the Tang result \cite{Ta}, if we assume the weight $w$ is in the Muckenhoupt $A_{1}$-class.

math.FA↗
arXiv2016

Fractional operators on weighted Morrey spaces

A necessary condition and a sufficient condition for one weight norm inequalities on Morrey spaces to hold are given for the fractional maximal operator and the fractional integral operator. We clarify the difference between the behavior of the fractional maximal operator and the one of the fractional integral operator which is originated from the structure of Morrey spaces. Both the necessary condition and the sufficient condition are also verified for the power weights.

math.FA↗
arXiv2015

The $n$ linear embedding theorem

Let $σ_i$, $i=1,\ldots,n$, denote positive Borel measures on $\mathbb{R}^d$, let $\mathcal{D}$ denote the usual collection of dyadic cubes in $\mathbb{R}^d$ and let $K:\,\mathcal{D}\to[0,\infty)$ be a~map. In this paper we give a~characterization of the $n$ linear embedding theorem. That is, we give a~characterization of the inequality $$ \sum_{Q\in\mathcal{D}} K(Q)\prod_{i=1}^n\left|\int_{Q}f_i\,dσ_i\right| \le C \prod_{i=1}^n \|f_i\|_{L^{p_i}(dσ_i)} $$ in terms of multilinear Sawyer's checking condition and discrete multinonlinear Wolff's potential, when $1<p_i<\infty$.

math.CA↗
arXiv2014

The Fatou property of block spaces

Around thirty years ago, block spaces, which are the predual of Morrey spaces, had been considered. However, it seems that there is no proof that block spaces satisfy the Fatou property. In this paper the Fatou property for block spaces is verified and the predual of block spaces is characterized.

math.CA↗