L^p(R^n)~N中的拟微分算子与正则半群

PSEUDODIFFERENTIAL OPERATORS AND REGULARIZED SEMIGROUPS ON L^p(R^n)~N

设 OPp( f )是 Lp( Rn) N( 1≤ p <∞ )中具有象征 f∈ Smp,0 的常系数拟微分算子 ,其中f( ζ)≡ ( fij( ζ) )是一个 N× N矩阵且 fij∈ C∞ ( Rn) .我们证明当象征 f 和它的导数满足某些增长条件时 ,OPp( f)在 Lp( Rn) N

Let OP p(f) be a pseudodifferential operator with symbol f∈S m ρ,0 having constant coefficients on L p(R n) N(1p<∞), where f(ζ)≡(f ij (ζ)) is a N×N matrix and f ij ∈C ∞(R n) . We prove that OP p(f) on L p(R n) N generates a differential regularized semigroup.