Higher order fractional Leibniz rule

DOI10.1007/s00041-017-9541-yzbMath1400.46027arXiv1609.05739OpenAlexW2523520355WikidataQ123116842 ScholiaQ123116842MaRDI QIDQ1645271

Kazumasa Fujiwara, Tohru Ozawa, Vladimir Georgiev

Publication date: 28 June 2018

Published in: The Journal of Fourier Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1609.05739

zbMATH Keywords

fractional derivativeLeibniz ruleKato-Ponce inequality

Mathematics Subject Classification ID

Maximal functions, Littlewood-Paley theory (42B25) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35)

Related Items (19)

Short-range scattering of Hartree type fractional NLS. II. ⋮ Weighted endpoint fractional Leibniz rule ⋮ A short proof of commutator estimates ⋮ Global well-posedness for the 2D Euler-Boussinesq-Bénard equations with critical dissipation ⋮ The Leibniz rule for the Dirichlet and the Neumann Laplacian ⋮ Local well-posedness of Dirac equations with nonlinearity derived from honeycomb structure in 2 dimensions ⋮ Regularity and stability of finite energy weak solutions for the Camassa-Holm equations with nonlocal viscosity ⋮ Large time behavior and convergence for the Camassa-Holm equations with fractional Laplacian viscosity ⋮ Local well-posedness for fourth order Benjamin-Ono type equations ⋮ On fractional Leibniz rule for Dirichlet Laplacian in exterior domain ⋮ Uniqueness in the Calderón problem and bilinear restriction estimates ⋮ Leibniz-type rules for bilinear and biparameter Fourier multiplier operators with applications ⋮ Well-posedness and scattering of inhomogeneous cubic-quintic NLS ⋮ Leibniz-type rules for bilinear Fourier multiplier operators with Besov regularity ⋮ Modified Scattering for the Cubic Schrödinger Equation Small Data Solution on Product Space ⋮ Breaking symmetry in focusing nonlinear Klein-Gordon equations with potential ⋮ The Kato-Ponce inequality with polynomial weights ⋮ Well-posedness and blow-up properties for the generalized Hartree equation ⋮ Remark on the Chain rule of fractional derivative in the Sobolev framework

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