Some notes on endpoint estimates for pseudo-differential operators

2022/01/26 by Guo, Jingwei, Zhu, Xiangrong
#35S05 #42B37 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2201.10724

Abstract

We study the pseudo-differential operator T_a f(x)=∫_ℝⁿe^ix⋅ξa(x,ξ)\widehatf(ξ) \textrmdξ, where the symbol a is in the Hörmander class S^m_ρ,1 or more generally in the rough Hörmander class L^∞S^m_ρ with m∈ℝ and ρ∈ [0,1]. It is known that T_a is bounded on L¹(ℝⁿ) for m

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