PreprintCC BY 4.0HAL
A boundedness result for degenerate parabolic Riesz transforms with rough coefficients
Abstract
In this paper, we prove a boundedness result for parabolic Riesz transforms in the range p ≤ 2 associated with degenerate parabolic operators whose elliptic part is in divergence form with complex coefficients depending measurably on space and time. The degeneracy is determined by a spatial weight in the Muckenhoupt class A2(ℝn). The argument relies on off-diagonal estimates for the parabolic gradient of the resolvent family, together with weighted embeddings. We obtain boundedness in a range of exponents strictly below $2$, with explicit ranges quantified by the reverse H\"older class of the weight. For real coefficients, this quantification is sharp and extends down to $1$.
Related
- Energy stability of explicit--implicit--null time discretizations for nonlinear degenerate parabolic equations with state-dependent coefficients
- Boundedness of Multilinear Hilbert Transforms Along Moment Curves
- Some New Sharp Boundedness Result Concerning Linear functionals on Banach spaces
- A connectedness result for convex polynomial multi-objective optimization without boundedness
- ℛ-boundedness of Riesz transforms and spectral multipliers of Schrödinger operators
BibTeX
@misc{baadi2026boundedness,
title = {{A boundedness result for degenerate parabolic Riesz transforms with rough coefficients}},
author = {Khalid Baadi},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21949},
eprint = {2609.21949},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05755263v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A boundedness result for degenerate parabolic Riesz transforms with rough coefficients
AU - Khalid Baadi
PY - 2026
DA - 2026/09/18
PB - HAL
DO - 10.48550/arxiv.2609.21949
UR - https://hal.science/hal-05755263v1
AB - In this paper, we prove a boundedness result for parabolic Riesz transforms in the range p ≤ 2 associated with degenerate parabolic operators whose elliptic part is in divergence form with complex coefficients depending measurably on space and time. The degeneracy is determined by a spatial weight in the Muckenhoupt class A_2(ℝ^n). The argument relies on off-diagonal estimates for the parabolic gradient of the resolvent family, together with weighted embeddings. We obtain boundedness in a range of exponents strictly below $2$, with explicit ranges quantified by the reverse H\"older class of the weight. For real coefficients, this quantification is sharp and extends down to $1$.
ER -