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Morrey Spaces on Domains: Different Approaches and Growth Envelopes.

ABSTRACT: We deal with Morrey spaces on bounded domains \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Omega $$\end{document}Ω obtained by different approaches. In particular, we consider three settings \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {M}_{u,p}(\Omega )$$\end{document}Mu,p(Ω), \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {M}_{u,p}(\Omega )$$\end{document}Mu,p(Ω) and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathfrak {M}_{u,p}(\Omega )$$\end{document}Mu,p(Ω), where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0

SUBMITTER: Haroske DD

PROVIDER: S-EPMC6294180 | biostudies-other | 2018

REPOSITORIES: biostudies-other

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Project description:IntroductionThe neural substrates of states devoted to processing self-related information ("self-related states") remain not fully elucidated. Besides the complexity of the problem, there is evidence suggesting that self-related states vary according to the information domain being considered. Here, we investigated brain correlates for self-related states concerning historical aspects of one's life (autobiographical self), and one's ongoing body status (core self). We focused on memory-related regions, body-related regions, CMSs (cortical midline structures), and ICs (insular cortices).MethodsThis was a block-design fMRI study contrasting brain activity for core self (interoception and exteroception) and autobiographical self (personality traits and biographic facts) information domains. It involved 19 participants, who answered questions about each domain (four conditions).ResultsAll conditions appeared to engage the regions of interest. Nonetheless, autobiographical self compared with core self showed greater activity in memory-related regions (e.g., hippocampus), MPFC (medial prefrontal cortex), superior PMC (posteromedial cortex), and anterior ICs. Core self compared with autobiographical self was associated with greater activity in body-related regions (e.g., somatosensory cortices, and EBA [extrastriate body area]), superior PMC, and posterior ICs. In addition, (1) facts compared with traits showed greater activity in body-related regions, memory-related regions, MPFC, and PMC; (2) traits compared with facts were associated with greater activity in the posterior part of the anterior cingulate cortex; (3) interoception compared with exteroception was associated with greater activity in body-related regions (e.g. postcentral gyrus), memory-related regions, MPFC, inferior PMC and ICs; (4) exteroception compared with interoception showed greater activity in some body-related regions (e.g., premotor cortices and EBA) and superior PMC.ConclusionsThe results support the notion that the neural correlates of self-related states depend on the information domain. Those states seem distinguishable in terms of activity in memory-related and body-related regions, and activity in regions that have been associated with self processes (CMSs and the ICs).

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Morrey Spaces on Domains: Different Approaches and Growth Envelopes.

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