Kernel smoothing operators on thick open domains
Abstract
We study the convergence properties of a general family of normalized Markovian kernels on a domain $$\Omega$$ in the Euclidean space. Based on the notion of a thick set we show that a local Hardy-Littlewood inequality holds in $$L^p(\Omega)$$ , $$p \in (1, \infty]$$ when $$\Omega$$ is thick. We then establish pointwise and $$L^p(\Omega)$$ convergence for families of convolution operators with a Markov normalization on $$\Omega$$ . We further discuss convergence properties of bistochastic kernels where the corresponding integral operators preserve constant functions and integrals.
Fields of Study & Subjects
Numerical methods in inverse problems
Advanced Mathematical Modeling in Engineering
Advanced Numerical Methods in Computational Mathematics
Publication details
- Journal / source
- Analysis Mathematica
- Publisher
- Springer Science and Business Media LLC
- Volume
- 52
- Issue
- 2
- Pages
- 493–516
- Publication date
- 1 June 2026
- Language
- EN