Calderón–Zygmund estimates in generalized Orlicz spaces

Hästö, Peter; Ok, Jihoon (2019-03-28)
 
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https://doi.org/10.1016/j.jde.2019.03.026

Hästö, Peter
Ok, Jihoon
Elsevier
28.03.2019

Peter Hästö, Jihoon Ok, Calderón–Zygmund estimates in generalized Orlicz spaces, Journal of Differential Equations, Volume 267, Issue 5, 2019, Pages 2792-2823, ISSN 0022-0396, https://doi.org/10.1016/j.jde.2019.03.026

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© 2019. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/.
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doi:https://doi.org/10.1016/j.jde.2019.03.026
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Abstract

We establish the \(W^{2,\varphi(⋅)}\)-solvability of the linear elliptic equations in non-divergence form under a suitable, essentially minimal, condition of the generalized Orlicz function \(\varphi(⋅)=\varphi(x,t)\), by deriving Calderón–Zygmund type estimates. The class of generalized Orlicz spaces we consider here contains as special cases classical Lebesgue and Orlicz spaces, as well as non-standard growth cases like variable exponent and double phase growth.

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