科研之友
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摘要
In this paper, we study the Fourier multiplier operator e(i mu(D)) on homogeneous Besov spaces (B) over dot(p,q)(s). If mu is a homogeneous function with positive degree whose Hessian matrix is non-degenerate at some point, we find the necessary conditions of p(i) q(i), s(i) (i = 1,2) for the boundedness of e(i mu(D)) from (B) over dot(p1,q1)(s1) to (B) over dot(p2,q2)(s2). Moreover, under a global non-degenerate assumptions on the Hessian matrix of mu(xi), we obtain the sufficient and necessary conditions for the boundedness of e(i mu(D)) between (B) over dot(p1,q1)(s1) and (B) over dot(p2,q2)(s2). More precisely, we obtain the estimates of the operator norm parallel to e(i mu(D))parallel to((B) over dotp1,q1s1 -> (B) over dotp2,q2s2), and get the blowup rate near singularity points.
