The boundedness of multilinear Calderón–Zygmund operators on Hardy spaces

Conditions for boundedness into Hardy spaces

“…Additional proofs of these results were provided by Grafakos and Li [10], Hu and Meng [13], and Huang and Liu [14]. All the aforementioned accounts on this topic are based on different…”

“…Additional approaches to these results were provided by Grafakos and Li , Hu and Meng , and Huang and Liu . In this work we investigate this topic via a new method based on ‐atomic decompositions.…”

“…approaches and address two classes of operators but [4], [13], and [14] seem to contain flaws in their proofs; in fact, as of this writing, only the approach in [10] stands, which deals with the case of finite sums of products of Calderón-Zygmund operators. In this work we revisit this line of investigation via a new method based on (p, ∞)-atomic decompositions.…”

“…In [1] boundedness was extended to 1 × 2 → for the entire range 0 < 1 , 2 , < ∞ and 1∕ = 1∕ 1 + 1∕ 2 , under the necessary cancellation conditions. Additional approaches to these results were provided by Grafakos and Li [9], Hu and Meng [13], and Huang and Liu [14]. In this work we investigate this topic via a new method based on ( , ∞)-atomic decompositions.…”

Multilinear fractional type operators and their commutators on Hardy spaces with variable exponents

“…In more recent years, the study of multilinear operators on Hardy space theory has received increasing attention by many authors, see for example [17,19,20]. While the multilinear operators worked well on the product of Hardy spaces, it is surprising that these similar results in the setting of variable exponents were unknown for a long time.…”