WebJan 26, 2016 · Erratum: Kato-Ponce inequalities on weighted and variable Lebesgue spaces. We prove fractional Leibniz rules and related commutator estimates in the settings of … Webavailable by the energy inequality) of the initial data, whereas the a priori energy bound depends on the Hsnorm. To prove the existence and uniqueness of solutions we use parabolic regularization and consider u t+ u xxxx+ u xxx+ uu x= 0: The energy inequality above remains intact since the contribution of the parabolic term is negative.
[1609.01780] On Kato-Ponce and fractional Leibniz - arXiv.org
WebAug 23, 2024 · This result, in particular, demonstrates that neither the classical Muckenhoupt weight condition nor the more general multilinear weight condition is required for the weighted Kato-Ponce inequality. We also consider a few other variants such as commutator and mixed norm estimates, and analogous conclusions are derived. WebIntroduction and main result The following inequality appears to be missing from the vast literature on a class of inequalities known as Kato-Ponce inequalities or fractional Leibniz … the chedi hotel muscat
On an endpoint Kato-Ponce inequality Request PDF - ResearchGate
WebWe prove that the L∞ end-point Kato-Ponce inequality (Leibniz rule) holds for the fractional Laplacian operators D3 = (-Δ)s/2, Js = (1-Δ) s/2, s > 0. This settles a conjecture by Grafakos ... WebNov 18, 2013 · A remark on an endpoint Kato-Ponce inequality @article{Grafakos2013ARO, title={A remark on an endpoint Kato-Ponce inequality}, author={Loukas Grafakos and Diego Maldonado and Virginia Naibo}, journal={arXiv: Analysis of PDEs}, year={2013} } L. Grafakos, D. Maldonado, V. Naibo; Published 18 November 2013; Mathematics; arXiv: Analysis of … Web5 Biparameter Kato-Ponce inequality in the weighted mixed norm setting ..... 1520 References ..... 1525 1 Introduction Boundedness properties of fractional differential … the chedi ninghai