Bibliographic Details
| 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] |
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| Database: |
Engineering Source |
