On Weak-convergence in the Localized Hardy Spacesand its Application

Let (χ, d, μ) be a complete RD-space. Letρbe an admissible function onχ, which means thatρis a positive function onχand there exist positive constantsC 0andk 0such that, for anyx, y∈χ, ρ ( y ) ≤ C 0 [ ρ ( x ) ] 1 / ( 1 + k 0 ) [ ρ ( x ) + d ( x , y ) ] k 0 / ( 1 + k 0 ) . In this paper, we define a...

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Published inTaiwanese journal of mathematics Vol. 20; no. 4; pp. 897 - 907
Main Authors Duc, Dinh Thanh, Hung, Ha Duy, Ky, Luong Dang
Format Journal Article
LanguageEnglish
Published Mathematical Society of the Republic of China 01.08.2016
Subjects
Mathematical functions
Mathematical theorems
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ISSN1027-5487
2224-6851

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Summary:Let (χ, d, μ) be a complete RD-space. Letρbe an admissible function onχ, which means thatρis a positive function onχand there exist positive constantsC 0andk 0such that, for anyx, y∈χ, ρ ( y ) ≤ C 0 [ ρ ( x ) ] 1 / ( 1 + k 0 ) [ ρ ( x ) + d ( x , y ) ] k 0 / ( 1 + k 0 ) . In this paper, we define a space VMO ρ (χ) and show that it is the predual of the localized Hardy space H ρ 1 ( χ ) . introduced by Yang and Zhou [14]. Then we prove a version of the classical theorem of Jones and Journé [7] on weak*-convergence in H ρ 1 ( χ ) . As an application, we give an atomic characterization of H ρ 1 ( χ ) . 2010Mathematics Subject Classification.42B35. Key words and phrases. H 1, BMO, VMO, Spaces of homogeneous type.
ISSN:1027-5487
2224-6851