Continuite-Besov des operateurs definis par des integrales singulieres

Our purpose is to give necessary and sufficient conditions for continuity, on Besov spaces \(\dot B_p^{s,q} \) , of singular integral operators whose kernels satisfy: $$|\partial _x^\alpha K(x, y)| \leqslant C_\alpha |x - y|^{ - n - |\alpha |} for|\alpha | \leqslant m,$$ where m ∈ ? and 0 < s < m. The criterion is compared to the M.Meyer theorem 11] where 0 _p ^s,q spaces for s?1. For 0 _p ^s,p space is characterized by the localization and by Besov-capacity. In particular we show that the BMO ₁ ^s,1 space is characterized by generalized Carleson conditions.