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Estimates for Lusin-area and Littlewood–Paley functions over spaces of homogeneous type

✍ Scribed by Yan Meng; Eiichi Nakai; Dachun Yang

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
1010 KB
Volume
72
Category
Article
ISSN
0362-546X

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Let X be a doubling metric measure space. If X has the δ-annular decay property for some δ ∈ (0, 1], the authors then establish the boundedness of the Lusin-area function, which is defined via kernels modeled on the semigroup generated by the Schrödinger operator, from localized spaces BMO ρ (X ) to

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## Abstract In this paper, we define an appropriate version of Morrey spaces for spaces of homogeneous type. As our main result, we give a sufficient condition for an operator to be bounded on the version of Morrey spaces (cf. Theorem 3.1 and Corollary 3.5). Moreover, using thin result, we prove Mo