Generally, the commutators of singular integrals and fractional integrals etc. with BMO functions are not bounded on Hardy spaces. However, for certain proper subspaces of BMO, the corresponding commutators can have well behaviors on the weighted Hardy spaces. In this talk, I'll present some recent results on the weighted Hp estimates for commutators of singular integrals and related operators with certain BMO functions, which include strongly singular integrals, fractional integrals, Marcinkiewicz integrals and variations associated to commutators of approximate identities.

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