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PreprintCC BY-NC 4.0HAL

FORM DOMINATION AND TENT SPACE ESTIMATES FOR OPERATORS ON THE HALF-SPACE

  • Pascal Auscher
  • Hedong Hou
  • Emiel Lorist
  • Andreas Rosén
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Abstract

We study operators acting on functions defined on the half-space, with methods inspired by sparse domination. Using the specific link between dyadic grids on the boundary and Whitney regions on the half-space, we obtain a very precise form domination with model operators of Hardy type. We introduce mixed-norm off-diagonal estimates that measures both tangential and transversal decay without requiring pointwise control in the transversal variable, substantially weakening the assumptions used in earlier tent space theories. This allows us to prove optimal weighted tent space extrapolation from local boundedness plus off-diagonal decay. The resulting framework yields new bounds for operators arising from non-autonomous elliptic and parabolic PDEs with non-smooth coefficients.

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Cite

BibTeXRIS
BibTeX
@misc{auscher2026form,
  title = {{FORM DOMINATION AND TENT SPACE ESTIMATES FOR OPERATORS ON THE HALF-SPACE}},
  author = {Pascal Auscher and Hedong Hou and Emiel Lorist and Andreas Rosén},
  howpublished = {HAL},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2609.29712},
  eprint = {2609.29712},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05733321v1},
  note = {CC BY-NC 4.0},
}
RIS
TY  - UNPB
TI  - FORM DOMINATION AND TENT SPACE ESTIMATES FOR OPERATORS ON THE HALF-SPACE
AU  - Pascal Auscher
AU  - Hedong Hou
AU  - Emiel Lorist
AU  - Andreas Rosén
PY  - 2026
DA  - 2026/08/31
PB  - HAL
DO  - 10.48550/arxiv.2609.29712
UR  - https://hal.science/hal-05733321v1
AB  - We study operators acting on functions defined on the half-space, with methods inspired by sparse domination. Using the specific link between dyadic grids on the boundary and Whitney regions on the half-space, we obtain a very precise form domination with model operators of Hardy type. We introduce mixed-norm off-diagonal estimates that measures both tangential and transversal decay without requiring pointwise control in the transversal variable, substantially weakening the assumptions used in earlier tent space theories. This allows us to prove optimal weighted tent space extrapolation from local boundedness plus off-diagonal decay. The resulting framework yields new bounds for operators arising from non-autonomous elliptic and parabolic PDEs with non-smooth coefficients.
ER  -