A singular integral operator related to block spaces

$L^p$ estimates for singular integrals with kernels belonging to certain block spaces

“…After the completion of our paper, we learned that these results on the operators T c,h and T * c,h had also been obtained by Al-Hasan and Fan (see [1] and [2]). …”

On the commutators of singular integrals related to block spaces

“…(ii) and (iii) are the special cases of (ii) and (iii) Lemma 2.2 in [1]. The proof of Lemma 3 is complete.…”

“…Later on, many application of the block decomposition to harmonic analysis were discovered (see [1], [14]- [16] etc.). For further background and information about the theory of spaces generated by blocks and its applications to harmonic analysis, one can consult the book [15].…”

Boundedness of higher order commutators of oscillatory singular integrals with rough kernels

“…Let Ω be a function homogeneous of degree zero with mean value zero on the unit sphere S n−1 . Define the oscillatory singular integral operator T by (1) T f (x) = p.v.…”

“…Later on, many applications of the block decomposition to harmonic analysis were discovered (see e.g. [1,11,12,13,14]). For further background and information about spaces generated by blocks and their applications to harmonic analysis, one can consult the book [12].…”