Some Function Spaces via Orthonormal Bases on Spaces of Homogeneous Type
Keyword(s):
Let(X,d,μ)be a space of homogeneous type in the sense of Coifman and Weiss, where the quasi-metricdmay have no regularity and the measureμsatisfies only the doubling property. Adapting the recently developed randomized dyadic structures ofXand applying orthonormal bases ofL2(X)constructed recently by Auscher and Hytönen, we develop the Besov and Triebel-Lizorkin spaces on such a general setting. In this paper, we establish the wavelet characterizations and provide the dualities for these spaces. The results in this paper extend earlier related results with additional assumptions on the quasi-metricdand the measureμto the full generality of the theory of these function spaces.
2019 ◽
Vol 63
(1)
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pp. 229-247
1988 ◽
Vol 309
(1)
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pp. 139-139
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1988 ◽
Vol 309
(1)
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pp. 139
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2013 ◽
Vol 34
(2)
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pp. 266-296
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2006 ◽
Vol 74
(3)
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pp. 347-358
2006 ◽
Vol 80
(2)
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pp. 229-262
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