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• Author or Editor: Feng Dai
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The maximal Fejér operator on real Hardy spaces

Periodica Mathematica Hungarica
Authors:
Gavin Brown
,
Dai Feng
, and
Ferenc Móricz

Abstract

We prove that the maximal Fej'er operator is not bounded on the real Hardy spaces H 1, which may be considered over
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathbb{T}$$ \end{document}
and
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathbb{R}$$ \end{document}
. We also draw corollaries for the corresponding Hardy spaces over
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathbb{T}$$ \end{document}
2 and
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathbb{R}$$ \end{document}
2.
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The maximal conjugate and Hilbert operators on real Hardy spaces

Acta Mathematica Hungarica
Authors:
Gavin Brown
,
Dai Feng
, and
Ferenc Móricz

We prove that the maximal conjugate and Hilbert operators are not bounded from the real Hardy space H 1 to L 1, where the underlying spaces may be over T or R. We also draw corollaries for the corresponding spaces over T 2 and R 2.

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Strong approximation by Fourier--Laplace series on the unit sphere S n-1

Acta Mathematica Hungarica
Authors:
Gavin Brown
,
Feng Dai
, and
Ferenc Móricz
Restricted access

LC-MS/MS assay for the therapeutic drug monitoring of perampanel in children with drug-resistant epilepsy

Acta Chromatographica
Authors:
Hao-ran Dai
,
Ya-hui Hu
,
Jia-yi Long
,
Ying Xia
,
Hong-li Guo
,
Jing Xu
,
Xuan-sheng Ding
,
Jing Chen
,
Xiao-peng Lu
, and
Feng Chen

Abstract

Perampanel (PER) is the first clinically available selective antagonist of α-amino-3-hydroxy-5-methylisoxazole-4-propionic acid (AMPA) receptor approved globally for the treatment of epilepsy. Studies have recently underlined the significant association between dose-exposure-effect-adverse events of PER in patients with epilepsy, so the therapeutic drug monitoring (TDM) of PER is critical in clinical practices, especially for pediatric patients with drug-resistant epilepsy. Due to several limits in previous published analytical methods, herein, we describe the development and validation of a novel liquid chromatography tandem mass spectrometry (LC-MS/MS) method for monitoring PER in human plasma samples. Protein precipitation method by acetonitrile containing PER-d5 as internal standard was applied for the sample clean-up. Formic acid (FA, 0.2 mM) in both aqueous water and acetonitrile were used as the mobile phases and the analyte was separated by an isocratic elution. Qualification and quantification were performed under positive electrospray ionization (ESI) mode using the m/z 350.3 → 219.1 and 355.3 → 220.0 ions pairs transitions for PER and PER-d5, respectively. Potential co-medicated anti-seizure medications (ASMs) have no interference to the analysis. Calibration curves were linear in the concentration range of 1.00–2,000 ng mL−1 for PER. The intra- and inter-batch precision, accuracy, recovery, dilution integrity, and stability of the method were all within the acceptable criteria and no matrix effect or carryover was found. This method was then successfully implemented on the TDM of PER in Chinese children with drug-resistant epilepsy. We firstly confirmed the apparent inter- and intra-individual PER concentration variabilities and potential drug-drug interactions between PER and several concomitant ASMs occurred in Chinese pediatric patients, which were also in line with previous studies in patients of other race.

Open access