Boundedness of Lusin-area and gλ* functions on localized Morrey-Campanato spaces over doubling metric measure spaces. Issue 3 (2011)

• Record Type: Journal Article
• Authors: Lin Lin, Haibo Haibo; Nakai Nakai, Eiichi Eiichi; Yang Yang, Dachun Dachun
• Other Names: Cobos Cobos Fernando Fernando Academic Editor.
• Is Part Of: Journal of function spaces and applications. Volume 9:Issue 3(2011)
• Page Start: 245
• Page End: 282
• Publication Date: 2011
• Subjects: Doubling metric measure space, Property (P), admissible function, Schrödinger operator, localized Morrey-Campanato space, Lusin-area function, g*λ function; Function spaces -- Periodicals; 515.73
• DOI: 10.1155/2011/187597
• Languages: English
• ISSNs: 0972-6802

Abstract

Abstract : Let χ be a doubling metric measure space and ρ an admissible function on χ . In this paper, the authors establish some equivalent characterizations for the localized Morrey-Campanato spaces ε ρ α, p ( χ ) and Morrey-Campanato-BLO spaces ε ̃ ρ α, p ( χ ) when α ∈ ( - ∞, 0 ) and p ∈ [ 1, ∞ ) . If χ has the volume regularity Property ( P ), 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 ε ρ a, p ( χ ) to ε ̃ ρ a, p ( χ ) without invoking any regularity of considered kernels. The same is true for the g λ * function and, unlike the Lusin-area function, in this case, χ is even not necessary to have Property ( P ) . These results are also new even for ℝ d with the d -dimensional Lebesgue measure and have a wide applications.