Abstract
Calderón–Zygmund operators are playing an important role in real analysis. The continuity of Calderón–Zygmund operators T on L2 was studied in [2–4] and, here, we are investigating the continuity of T on the Besov spaces [Formula: see text] where 1 ≤ p, q ≤ ∞ and on the Triebel–Lizorkin spaces [Formula: see text] where 1 ≤ p < ∞, 1 ≤ q ≤ ∞. The exponents measuring the regularity of the distributional kernel K(x, y) of T away from the diagonal are playing a key role in our results. They are smaller than the ones which were assumed by other authors. Moreover, our results are sharp in the case of the Besov spaces [Formula: see text] and of the Triebel–Lizorkin spaces [Formula: see text] when 1 ≤ q ≤ ∞. The proof uses a pseudo-annular decomposition of Calderón–Zygmund operators.
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