Lᵖ-continuity for Calderón--Zygmund operator
Yang, Q X
Original · EN
Given a Calderón--Zygmund (C--Z for short) operator T, which satisfies Hörmander condition, we prove that: if T maps all the characteristic atoms to WL¹, then T is continuous from Lᵖ to Lᵖ(1<p<∞). So the study of strong continuity on arbitrary function in Lᵖ has been changed into the study of weak continuity on characteristic functions.
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