Bilinear estimates in Besov spaces generated by the Dirichlet Laplacian
Tsukasa Iwabuchi, Tokio Matsuyama, Koichi Taniguchi
TL;DR
This paper establishes bilinear estimates in Besov spaces generated by the Dirichlet Laplacian, utilizing heat semigroup gradient estimates, Bony paraproducts, and spectral multiplier boundedness.
Contribution
It introduces new bilinear estimates in Besov spaces associated with the Dirichlet Laplacian on Euclidean domains, expanding the analytical tools available for PDEs.
Findings
Proved bilinear estimates in Besov spaces for the Dirichlet Laplacian.
Utilized gradient estimates of heat semigroup and Bony paraproduct formula.
Demonstrated boundedness of spectral multipliers in this context.
Abstract
The purpose of this paper is to establish bilinear estimates in Besov spaces generated by the Dirichlet Laplacian on a domain of Euclidian spaces. These estimates are proved by using the gradient estimates for heat semigroup together with the Bony paraproduct formula and the boundedness of spectral multipliers.
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Advanced Mathematical Physics Problems · Nonlinear Partial Differential Equations