LpSρ^m拟微分算子在Morrey空间上的估计

Estimate for LpSρ^m Pseudo-differential Operators on Morrey Spaces

该文给出了LpSρ^m拟微分算子在Morrey空间上的有界性.令1<r<∞,1<q<∞以及p≥2,并且满足1/r=1/p+1/q.假设0<κ<1/q,ρ≤1,a(x,ξ)∈LpSρ^m是拟微分算子Ta的象征,则对于m<n(ρ-1)p′,Ta是M r,rκ到M q,qκ有界的.

In this paper,we obtain boundedness of LpSρ^m pseudo-differential operators on the Morrey spaces.Let 1<r<∞,1<q<∞and p≥2 with 1/r=1/p+1/q.Suppose 0<κ<1/q,ρ≤1 and a(x,ξ)∈LpSρ^m is a symbol of pseudo-differential operators T a.Then T a is bounded from M r,rκinto M q,qκprovided m<n(ρ-1)p′.