$H^{p}$ estimates for weakly strongly singular integral operators on spaces of homogeneous type

On the continuity of strongly singular Calderón-Zygmund-type operators on Hardy spaces

“…However, for operators associated to δ − kernels of type σ the classical definition of molecules does not apply in an effective way for this purpose and a notion of molecules that best fit these types of operators is necessary. Such ideas were originally explored by B. Bordin [4], J. Álvarez and M. Milman [2].…”

Weighted norm inequalities for multilinear strongly singular Calderón–Zygmund operators on RD‐spaces

“…[13, 22, 42, 44]) and were referred to as weakly–strongly singular integral operators by C. Fefferman in [13]. Inspired by these results, and the work of Macías and Segovia [39] and Bordin [3], Alvarez and Milman considered the theory of strongly singular Calderón–Zygmund operators in the case of scalar and vector values in [1] and [2], respectively. Their results included $$L^p$$, $$H^p$$, and $$BMO$$ continuity and they also showed that the class of strongly singular Calderón–Zygmund operators include the pseudo‐differential operator with symbol in the Hörmander's class $$S^{-\beta }_{\alpha , \delta }(\mathbb {R}^n)$$ where $$0<\delta \le \alpha <1$$ and $$n(1-\alpha )/2\le \beta <n/2$$.…”