Skip to content
DraconiticResearch
Search Sources API
186,541 studies31 sourcesUpdated 57 min ago
PreprintCC BY-NC-ND 4.0arXiv

Sharp Volume-Based Bounds for BMO Functions on Compact Domains and Applications

  • Marin Mišur
Open at sourcePDFDOICite

Abstract

We establish sharp localized Lr bounds for compactly supported functions of bounded mean oscillation (BMO). Classical estimates obtained via the John-Nirenberg inequality bound the Lr norm of such a function in terms of the diameter of its support. We show that the diameter dependence can be replaced by the Lebesgue measure of the support, the relevant quantity for thin, highly eccentric domains. The proof relies on non-increasing rearrangements and the Bennett-DeVore-Sharpley theorem, and requires no vanishing-oscillation hypothesis. We present physical and operator-theoretic applications: geometric collapse in tubular neighborhoods, a localized Cwikel-Lieb-Rozenblum bound for Schrödinger operators, and decoupling bounds for the localized action of Calderón-Zygmund singular integrals.

Related

  1. Bounds for the residue of Dedekind zeta functions under GRH and applications
    Stephan Ramon Garcia, Loïc Grenié, Ethan Simpson Lee +1
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  2. Regular Arithmetic Functions, Volume I. Theory, Applications, Examples
    Benoit Cloitre
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  3. Finite volume quotients of bounded domains with piecewise smooth boundary
    Xingsi Pu, Lang Wang
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  4. Surface-to-Volume Homogenization of NonLinear Steklov Eigencouples with NonHomogeneous Orlicz Growth in Perforated Domains
    Hermann Douanla, Hubert Nnang, Joel Fotso Tachago +1
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  5. A Comparative Study of Finite-Volume-based Coupled and Segregated Reduced-Order Models for Incompressible Flows in Parametrized Domains
    Andrea Buffolini, Davide Oberto, Gianluigi Rozza
    arXivPreprintCC BY 4.0Full textNumerical analysis & scientific computingFluid dynamicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{misur2026sharp,
  title = {{Sharp Volume-Based Bounds for BMO Functions on Compact Domains and Applications}},
  author = {Marin Mišur},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.11467},
  eprint = {2609.11467},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.11467},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Sharp Volume-Based Bounds for BMO Functions on Compact Domains and Applications
AU  - Marin Mišur
PY  - 2026
DA  - 2026/09/10
PB  - arXiv
DO  - 10.48550/arxiv.2609.11467
UR  - https://arxiv.org/abs/2609.11467
AB  - We establish sharp localized L^r bounds for compactly supported functions of bounded mean oscillation (BMO). Classical estimates obtained via the John-Nirenberg inequality bound the L^r norm of such a function in terms of the diameter of its support. We show that the diameter dependence can be replaced by the Lebesgue measure of the support, the relevant quantity for thin, highly eccentric domains. The proof relies on non-increasing rearrangements and the Bennett-DeVore-Sharpley theorem, and requires no vanishing-oscillation hypothesis. We present physical and operator-theoretic applications: geometric collapse in tubular neighborhoods, a localized Cwikel-Lieb-Rozenblum bound for Schrödinger operators, and decoupling bounds for the localized action of Calderón-Zygmund singular integrals.
ER  -