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Embeddings of weighted generalized Morrey Spaces into Lebesgue Spaces on fractal sets

Permanent link
https://hdl.handle.net/10037/17364
DOI
https://doi.org/10.1515/fca-2019-0064
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Published version (PDF)
Date
2019-12-19
Type
Journal article
Tidsskriftartikkel
Peer reviewed

Author
Samko, Natasha Gabatsuyevna
Abstract
We study embeddings of weighted local and consequently global generalized Morrey spaces defined on a quasi-metric measure set (X, d, μ) of general nature which may be unbounded, into Lebesgue spaces Ls(X), 1 ≤ s ≤ p < ∞. The main motivation for obtaining such an embedding is to have an embedding of non-separable Morrey space into a separable space. In the general setting of quasi-metric measure spaces and arbitrary weights we give a sufficient condition for such an embedding. In the case of radial weights related to the center of local Morrey space, we obtain an effective sufficient condition in terms of (fractional in general) upper Ahlfors dimensions of the set X. In the case of radial weights we also obtain necessary conditions for such embeddings of local and global Morrey spaces, with the use of (fractional in general) lower and upper Ahlfors dimensions. In the case of power-logarithmic-type weights we obtain a criterion for such embeddings when these dimensions coincide.
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Published version, available 12 months embargo from published date.
Publisher's version: https://www.degruyter.com/downloadpdf/j/fca.2019.22.issue-5/fca-2019-0064/fca-2019-0064.pdf
Publisher
De Gruyter
Citation
Samko, N. (2019) Embeddings of weighted generalized Morrey Spaces into Lebesgue Spaces on fractal sets. Fractional Calculus and Applied Analysis, 22, (5), 1203-1224.
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