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Sobolev embedding into BMO and weak-[formula omitted] for 1-dimensional probability measure.

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Title: Sobolev embedding into BMO and weak-[formula omitted] for 1-dimensional probability measure.
Authors: Feo, Filomena1 filomena.feo@uniparthenope.it, Martin, Joaquim2 jmartin@mat.uab.cat, Posteraro, M. Rosaria3 posterar@uniparthenope.it
Source: Journal of Mathematical Analysis & Applications. Feb2015, Vol. 422 Issue 1, p478-495. 18p.
Subjects: Sobolev spaces, Embeddings (Mathematics), Bounded mean oscillation, Dimensional analysis, Probability measures, Rearrangement invariant spaces, Probability theory
Abstract: We characterize rearrangement invariant spaces X with respect to a suitable 1-dimensional probability μ ( e.g. log-concave measure) such that the Sobolev embedding ‖ u ‖ BMO ( R , μ ) ≤ C ( ‖ u ′ ‖ X + ‖ u ‖ L 1 ( R , μ ) ) holds for any function u ∈ L 1 ( R , μ ) , whose real-valued weakly derivative u ′ belongs to X . Here BMO ( R , μ ) is the space of functions with bounded mean oscillation with respect to μ . We investigate the embedding in weak- L ∞ ( R , μ ) , too. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Mathematical Analysis & Applications is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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DbLabel: Engineering Source
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  Data: Sobolev embedding into BMO and weak-[formula omitted] for 1-dimensional probability measure.
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  Data: <searchLink fieldCode="AR" term="%22Feo%2C+Filomena%22">Feo, Filomena</searchLink><relatesTo>1</relatesTo><i> filomena.feo@uniparthenope.it</i><br /><searchLink fieldCode="AR" term="%22Martin%2C+Joaquim%22">Martin, Joaquim</searchLink><relatesTo>2</relatesTo><i> jmartin@mat.uab.cat</i><br /><searchLink fieldCode="AR" term="%22Posteraro%2C+M%2E+Rosaria%22">Posteraro, M. Rosaria</searchLink><relatesTo>3</relatesTo><i> posterar@uniparthenope.it</i>
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Mathematical+Analysis+%26+Applications%22">Journal of Mathematical Analysis & Applications</searchLink>. Feb2015, Vol. 422 Issue 1, p478-495. 18p.
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  Data: <searchLink fieldCode="DE" term="%22Sobolev+spaces%22">Sobolev spaces</searchLink><br /><searchLink fieldCode="DE" term="%22Embeddings+%28Mathematics%29%22">Embeddings (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Bounded+mean+oscillation%22">Bounded mean oscillation</searchLink><br /><searchLink fieldCode="DE" term="%22Dimensional+analysis%22">Dimensional analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Probability+measures%22">Probability measures</searchLink><br /><searchLink fieldCode="DE" term="%22Rearrangement+invariant+spaces%22">Rearrangement invariant spaces</searchLink><br /><searchLink fieldCode="DE" term="%22Probability+theory%22">Probability theory</searchLink>
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  Data: We characterize rearrangement invariant spaces X with respect to a suitable 1-dimensional probability μ ( e.g. log-concave measure) such that the Sobolev embedding ‖ u ‖ BMO ( R , μ ) ≤ C ( ‖ u ′ ‖ X + ‖ u ‖ L 1 ( R , μ ) ) holds for any function u ∈ L 1 ( R , μ ) , whose real-valued weakly derivative u ′ belongs to X . Here BMO ( R , μ ) is the space of functions with bounded mean oscillation with respect to μ . We investigate the embedding in weak- L ∞ ( R , μ ) , too. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Mathematical Analysis & Applications is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1016/j.jmaa.2014.08.045
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      – Code: eng
        Text: English
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        PageCount: 18
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    Subjects:
      – SubjectFull: Sobolev spaces
        Type: general
      – SubjectFull: Embeddings (Mathematics)
        Type: general
      – SubjectFull: Bounded mean oscillation
        Type: general
      – SubjectFull: Dimensional analysis
        Type: general
      – SubjectFull: Probability measures
        Type: general
      – SubjectFull: Rearrangement invariant spaces
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      – SubjectFull: Probability theory
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      – TitleFull: Sobolev embedding into BMO and weak-[formula omitted] for 1-dimensional probability measure.
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            NameFull: Martin, Joaquim
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            NameFull: Posteraro, M. Rosaria
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              Text: Feb2015
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