科研之友
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摘要
In this paper, we study the generalized commutators of Sjolin type operator T-alpha,A(a,m) defined by @@@ T(alpha,A)(a,m)f(x) = integral(Rn) K-alpha(a)(x - y) R-m(A; x,y)/vertical bar x - y vertical bar(m-1) f(y)dy = integral(Rn)e(i)vertical bar x - y vertical bar(a)/vertical bar x - y vertical bar(alpha) R-m(A; x, y)/vertical bar x - y vertical bar(m-1) f(y)dy, @@@ where R-m(A; x, y) = A(x) - Sigma(vertical bar alpha vertical bar<m) 1/alpha! D-alpha A(y)(x - y)(alpha) with m is an element of Z(+). @@@ By using the scale changing method, we prove that if D(gamma)A is an element of (Lambda) over dot(beta) (0 < beta < 1) with vertical bar gamma vertical bar = m - 1, m >= 2 or A is an element of(Lambda) over dot(beta) (0 < beta < 1) when m = 1, T-alpha,A(a,m) is bounded on L-p(R-n) for certain range of p.
