Generalizations of Calderón-Zygmund operators

Weighted Norm Inequalities for Paraproducts and Bilinear Pseudodifferential Operators with Mild Regularity

“…This follows from the fact that T 1 h and T 2 h are linear Calderón-Zygmund operators of type ω(t) as described in Yabuta [46], where these boundedness properties are proved. ).…”

“…VII]. Notice that the class of forbidden symbols S 0 1,1 satisfies S 0 1,1 ⊂ S 0 1,ω 0 , 0 , where ω 0 (t) = t and 0 (t) = 1 + t. In [46], [47] and [48], K. Yabuta developed the notion of Calderón-Zygmund operator of type ω(t) (which includes the classical Calderón-Zygmund operators) and determined conditions on a symbol σ ∈ S 0 1,ω, and on the functions ω, , so that T σ can be realized as a Calderón-Zygmund operator of type ω(t). As a consequence, he also obtained L ∞ -BMO and weighted L p -estimates for T σ .…”

“…The class BS 0 1,1 produces bilinear DOs with bilinear Calderón-Zygmund kernels in the sense of L. Grafakos and R. Torres [25], and, as proved by Á. Bényi and R. Torres [4], it also remains forbidden. Here we implement a bilinear interpretation of Yabuta's scheme [46,47]. In Sect.…”

Commutators of multilinear Calderón–Zygmund operators with Dini type kernels on some function spaces

“…Then many researchers were interested in bilinear or multilinear singular integrals (see [3, 5-11, 21, 22]). During the same period some generalizations of Calderón-Zygmund operators were also studied by many authors such as Calderón-Zygmund operators with kernels of type ω which was first studied by Yabuta [20] in 1985. Maldonado and Naibo [12] studied the bilinear Calderón-Zygmund operators of type ω in 2009.…”

Riesz transform characterizations of Musielak-Orlicz-Hardy spaces

“…Recall the following notion of θ-Calderón-Zygmund operators from Yabuta [43]. Let θ be a nonnegative nondecreasing function on (0, ∞) satisfyinǵ…”