1983
DOI: 10.4064/sm-75-2-217-234
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$H^{p}$ estimates for weakly strongly singular integral operators on spaces of homogeneous type

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Cited by 7 publications
(2 citation statements)
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“…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].…”
Section: Generalized Moleculesmentioning
confidence: 99%
“…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].…”
Section: Generalized Moleculesmentioning
confidence: 99%
“…[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 Lp$L^p$, Hp$H^p$, and BMO$BMO$ 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 Sα,δβ(double-struckRn)$S^{-\beta }_{\alpha , \delta }(\mathbb {R}^n)$ where 0<δα<1$0&lt;\delta \le \alpha &lt;1$ and nfalse(1αfalse)/2β<n/2$n(1-\alpha )/2\le \beta &lt;n/2$.…”
Section: Introductionmentioning
confidence: 99%