Multipliers spaces and pseudo-differential operators

2005/05/02 by Sadek Gala, Gala, Sadek
Mathematics · #31Bxx #42Bxx #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Analysis and Transform Methods #advanced mathematical theories #math.AP #msc:31Bxx #msc:42Bxx

paper · pdf · doi:10.48550/arxiv.math/0505021

arxiv created 2005/05/02 · openalex publication_date 2005/05/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let σ(x,ξ) be a sufficiently regular function defined on R^d × R^d. The pseudo-differential operator with symbol σ is defined on the Schwartz class by the formula: f→σf(x)=∫_R^d σ(x,ξ) f(ξ)e^2πixξdξ, where f(ξ)=∫_R^d f(x)e^-2πixξdx is the Fourier transform of f. In this paper, we shall consider the regularity of the following type : \begindescription \item[(a)] | ∂_ξ^ασ(x,ξ) | ≤ A_α(1+| ξ|) ^{-| α|}, \item[(b)] | ∂_ξ^ασ(x+y,ξ) -∂_ξ^ασ(x,ξ) | ≤ A_αω(| y|) (1+| ξ|) ^{-| α|}, \enddescription %

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