Type: Article
Publication Date: 1994-04-01
Citations: 175
DOI: https://doi.org/10.1112/jlms/49.2.296
For a Calderón-Zygmund singular integral operator T, we show that the following weighted inequality holds ∫ R n | T f ( y ) | p w ( y ) dy ⩽ C ∫ R n | f ( y ) | p M [ p ] + 1 w ( y ) dy , where Mk is the Hardy-Littlewood maximal operator M iterated k times, and [p] is the integer part of p. Moreover, the result is sharp since it does not hold for M[p]. We also give the following endpoints results: w ( { y ∈ R n : | Tf ( y ) | > λ } ) ⩽ C λ ∫ R n | f ( y ) | M 2 w ( y ) dy , and ∫ R n | T f ( y ) | w ( y ) dy ⩽ C ∥ f ∥ H 1 ( M w ) , where H1(μ) is the atomic Hardy space with respect to μ.