On Hardy-Littlewood-Sobolev estimates for degenerate Laplacians

2025/06/25 by Pascal Auscher, Auscher, Pascal, Khalid Baadi +1 · 1 citation
Mathematics · Computer Science · #Nonlinear Partial Differential Equations #Advanced Mathematical Modeling in Engineering #Advanced Harmonic Analysis Research

paper · pdf · doi:10.48550/arxiv.2506.20368

Abstract

We establish norm inequalities for fractional powers of degenerate Laplacians, with degeneracy being determined by weights in the Muckenhoupt class A₂(ℝⁿ), accompanied by specific additional reverse Hölder assumptions. This extends the known results for classical Riesz potentials. The approach is based on size estimates for the degenerate heat kernels. The approach also applies to more general weighted degenerate operators.

Citations

• On well-posedness for second-order degenerate parabolic equations with unbounded lower-order terms
• Degenerate parabolic equations in divergence form: fundamental solution and Gaussian bounds
• On fundamental solutions and Gaussian bounds for degenerate parabolic equations with time-dependent coefficients
• Extrapolation on function and modular spaces, and applications
• On necessary and sufficient conditions for L^p-estimates of Riesz transforms associated to elliptic operators on \RRⁿ and related estimates

Cited by

• On well-posedness for second-order degenerate parabolic equations with unbounded lower-order terms

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