Abstract
Let K be a generalized Calderón–Zygmund kernel defined on R n × ( R n ∖ { 0 } ) . The singular integral operator with variable kernel given by T f ( x ) = p.v. ∫ R n K ( x , x − y ) f ( y ) d y is studied. We show that if the kernel K ( x , y ) satisfies the L q -Hörmander condition with respect to x and y variables, respectively, then T is bounded on L w p . If we add an extra Dini type condition on K, then we may show the H w p − L w p boundedness of T.
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