Lp-continuity for Calderón-Zygmund operator
Given a Calderón-Zygmund (C-Z for short) operatorT, which satisfies Hörmander condition, we prove that: ifT maps all the characteristic atoms toWL1, thenT is continuous fromLp toLp(1 <p < ∞). So the study of strong continuity on arbitrary function inLp has been changed into the study of weak continuity on characteristic functions.
Volume 130, 2020
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