# Growth Envelopes of Some Variable and Mixed Function Spaces

@article{Haroske2022GrowthEO,
title={Growth Envelopes of Some Variable and Mixed Function Spaces},
author={Dorothee D. Haroske and Cornelia Schneider and Krist{\'o}f Szarvas},
journal={The Journal of Geometric Analysis},
year={2022},
volume={32},
pages={1-46}
}
• Published 16 July 2020
• Mathematics
• The Journal of Geometric Analysis
We study unboundedness properties of functions belonging to Lebesgue and Lorentz spaces with variable and mixed norms using growth envelopes. Our results extend the ones for the corresponding classical spaces in a natural way. In the case of spaces with mixed norms, it turns out that the unboundedness in the worst direction, i.e., in the direction where $$p_{i}$$ p i is the smallest, is crucial. More precisely, the growth envelope is given by {\mathfrak {E}}_{{\mathsf {G}}}(L_{\overrightarrow…
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