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arXiv · 2409.07395

A Dyadic Approach to Weak Characterizations of Function Spaces

Galia Dafni·Shahaboddin Shaabani
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Abstract

Weak-type quasi-norms are defined using the mean oscillation or the mean of a function on dyadic cubes, providing discrete analogues and variants of the corresponding quasi-norms on the upper half-space previously considered in the literature. Comparing the resulting function spaces to known function spaces such as $\dot{W}^{1,p}(\rn)$, $\JNp$, $\Lp$ and weak-$\Lp$ gives new embeddings and characterizations of these spaces. Examples are provided to prove the sharpness of the results.

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BibTeXRIS

Galia Dafni, Shahaboddin Shaabani. 2024-09-11. A Dyadic Approach to Weak Characterizations of Function Spaces. https://arxiv.org/abs/2409.07395

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