Acta mathematica scientia, Series B >
A NOTE ON SINGULAR INTEGRALS WITH DOMINATING MIXED SMOOTHNESS IN TRIEBEL-LIZORKIN SPACES
Received date: 2012-01-06
Revised date: 2013-04-02
Online published: 2014-07-20
Let h be a measurable function defined on R+×R+. Let Ω∈ L(log L+)νq (Sn1−1×Sn2−1) (1 ≤ νq ≤2) be homogeneous of degree zero and satisfy certain cancellation condi-tions. We show that the singular integral
Tf(x1, x2) = p. v.∫∫Rn1+n2 Ω(y´1, y´2)h(|y1|, |y2|)/|y1|n1 |y2|n2 f(x1 − y1, x2 − y2)dy1dy2
maps from Sα1, α2p, qF(Rn1 × Rn2 ) boundedly to itself for 1 < p, q <∞, α1, α2 ∈R.
Hung Viet LE . A NOTE ON SINGULAR INTEGRALS WITH DOMINATING MIXED SMOOTHNESS IN TRIEBEL-LIZORKIN SPACES[J]. Acta mathematica scientia, Series B, 2014 , 34(4) : 1331 -1344 . DOI: 10.1016/S0252-9602(14)60087-4
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