Extension of Olsen\u27s inequality to Morrey-Lorentz spaces

【学位授与の要件】中央大学学位規則第4条第1項【論文審査委員主査】澤野　嘉宏（中央大学理工学部教授）【論文審査委員副査】松山　登喜夫（中央大学理工学部教授）、津川　光太郎（中央大学理工学部教授）、香取　眞理（中央大学理工学部教授）、中井　英一（茨城大学理工学研究科教授）博士(理学)中央大

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.Comment: 12 page

Sparse non-smooth atomic decomposition of quasi-Banach lattices

A theory of non-smooth atomic decomposition is obtained fora large class of quasi-Banach lattices, including Morrey spaces, Lorentzspaces, mixed Lebesgue spaces as well as some related function spaces.As an application, an inequality comparing the fractional maximal operatorand the fractional integral operator is considered. Some examplesshow that the restriction posed on quasi-Banach lattices are indispensable.This paper, which is a follow-up of the third author’s paper in2020, simplifies the proof of some existing results

Regulation of Ca2+/calmodulin-dependent protein kinase kinase beta by cAMP signaling

BACKGROUND: Ca2+/calmodulin-dependent protein kinase kinase (CaMKK) is a pivotal activator of CaMKI, CaMKIV and 5'-AMP-activated protein kinase (AMPK), controlling Ca2+-dependent intracellular signaling including various neuronal, metabolic and pathophysiological responses. Recently, we demonstrated that CaMKKβ is feedback phosphorylated at Thr144 by the downstream AMPK, resulting in the conversion of CaMKKβ into Ca2+/CaM-dependent enzyme. However, the regulatory phosphorylation of CaMKKβ at Thr144 in intact cells and in vivo remains unclear. METHODS: Anti-phosphoThr144 antibody was used to characterize the site-specific phosphorylation of CaMKKβ in immunoprecipitated samples from mouse cerebellum and in transfected mammalian cells that were treated with various agonists and protein kinase inhibitors. CaMKK activity assay and LC-MS/MS analysis were used for biochemical characterization of phosphorylated CaMKKβ. RESULTS: Our data suggest that the phosphorylation of Thr144 in CaMKKβ is rapidly induced by cAMP/cAMP-dependent protein kinase (PKA) signaling in CaMKKβ-transfected HeLa cells, that is physiologically relevant in mouse cerebellum. We confirmed that the catalytic subunit of PKA was capable of directly phosphorylating CaMKKβ at Thr144 in vitro and in transfected cells. In addition, the basal phosphorylation of CaMKKβ at Thr144 in transfected HeLa cells was suppressed by AMPK inhibitor (compound C). PKA-catalyzed phosphorylation reduced the autonomous activity of CaMKKβ in vitro without significant effect on the Ca2+/CaM-dependent activity, resulting in the conversion of CaMKKβ into Ca2+/CaM-dependent enzyme. CONCLUSION: cAMP/PKA signaling may confer Ca2+-dependency to the CaMKKβ-mediated signaling pathway through direct phosphorylation of Thr144 in intact cells. GENERAL SIGNIFICANCE: Our results suggest a novel cross-talk between cAMP/PKA and Ca2+/CaM/CaMKKβ signaling through regulatory phosphorylation