Composition and L²-boundedness of flag kernels

Paweł  Głowacki

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Correction to "Composition and L²-boundedness of flag kernels" (Colloq. Math. 118 (2010), 581-585)

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Yong Ding, Xinfeng Wu (2009)

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Let 𝔾 be a homogeneousgroup on ℝⁿ whose multiplication and inverse operations are polynomial maps. In 1999, T. Tao proved that the singular integral operator with Llog⁺L function kernel on ≫ is both of type (p,p) and of weak type (1,1). In this paper, the same results are proved for the Littlewood-Paley g-functions on 𝔾

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Chin-Cheng Lin (1996)

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We give sufficient conditions on the kernel K for the convolution operator Tf = K ∗ f to be bounded on Hardy spaces $H^{p} (G)$ , where G is a homogeneous group.

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2010 Mathematics Subject Classification: Primary 35L05. Secondary 46E35, 35J25, 22E30. In this paper we define the homogeneous Besov spaces associated with the Dunkl operators on R^d, and we give a complete analysis on these spaces and same applications.

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The Campanato, Morrey and Hölder spaces on spaces of homogeneous type

Eiichi Nakai (2006)

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We investigate the relations between the Campanato, Morrey and Hölder spaces on spaces of homogeneous type and extend the results of Campanato, Mayers, and Macías and Segovia. The results are new even for the ℝⁿ case. Let (X,d,μ) be a space of homogeneous type and (X,δ,μ) its normalized space in the sense of Macías and Segovia. We also study the relations of these function spaces for (X,d,μ) and for (X,δ,μ). Using these relations, we can show that theorems for the Campanato, Morrey or...