Robust near-diagonal green function estimates
M Kassmann, M Kim, KA Lee - … Mathematics Research Notices, 2023 - academic.oup.com
M Kassmann, M Kim, KA Lee
International Mathematics Research Notices, 2023•academic.oup.comWe prove sharp near-diagonal pointwise bounds for the Green function for nonlocal
operators of fractional order. The novelty of our results is two-fold: the estimates are robust
as and we prove the bounds without making use of the Dirichlet heat kernel. In this way, we
can cover cases, in which the Green function satisfies isotropic bounds but the heat kernel
does not.
operators of fractional order. The novelty of our results is two-fold: the estimates are robust
as and we prove the bounds without making use of the Dirichlet heat kernel. In this way, we
can cover cases, in which the Green function satisfies isotropic bounds but the heat kernel
does not.
Abstract
We prove sharp near-diagonal pointwise bounds for the Green function for nonlocal operators of fractional order . The novelty of our results is two-fold: the estimates are robust as and we prove the bounds without making use of the Dirichlet heat kernel . In this way, we can cover cases, in which the Green function satisfies isotropic bounds but the heat kernel does not.
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