( <i>q</i> , <i>p</i> )-Mixing Bloch maps

Abstract As a Bloch variant of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>q</m:mi> <m:mo>,</m:mo> <m:mi>p</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> \left(q,p) -mixing linear operators, we introduce the notion of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>q</m:mi> <m:mo>,</m:mo> <m:mi>p</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> \left(q,p) -mixing Bloch maps. We prove Pietsch’s domination theorem and Maurey’s splitting theorem in this Bloch context, following the corresponding results from the linear case.