کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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4592603 | 1335115 | 2008 | 50 صفحه PDF | دانلود رایگان |
Let s∈R, τ∈[0,∞), p∈(1,∞) and q∈(1,∞]. In this paper, we introduce a new class of function spaces which unify and generalize the Triebel–Lizorkin spaces with both p∈(1,∞) and p=∞ and Q spaces. By establishing the Carleson measure characterization of Q space, we then determine the relationship between Triebel–Lizorkin spaces and Q spaces, which answers a question posed by Dafni and Xiao in [G. Dafni, J. Xiao, Some new tent spaces and duality theorem for fractional Carleson measures and Qα(Rn), J. Funct. Anal. 208 (2004) 377–422]. Moreover, via the Hausdorff capacity, we introduce a new class of tent spaces and determine their dual spaces , where s∈R, p,q∈[1,∞), max{p,q}>1, , and t′ denotes the conjugate index of t∈(1,∞); as an application of this, we further introduce certain Hardy–Hausdorff spaces and prove that the dual space of is just when p,q∈(1,∞).
Journal: Journal of Functional Analysis - Volume 255, Issue 10, 15 November 2008, Pages 2760-2809