# 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} }

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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