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

### Calderón–Zygmund estimates in generalized Orlicz spaces

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Author: Hästö, Peter1,2; Ok, Jihoon3
Organizations: 1Department of Mathematics and Statistics, FI-20014 University of Turku, Finland
2Department of Mathematics, FI-90014 University of Oulu, Finland
3Department of Applied Mathematics and the Institute of Natural Sciences, Kyung Hee University, Yongin 17104, Republic of Korea
Format: article
Version: accepted version
Access: embargoed
Language: English
Published: Elsevier, 2019
Publish Date: 2021-03-28
Description:

# 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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Series: Journal of differential equations
ISSN: 0022-0396
ISSN-E: 1090-2732
ISSN-L: 0022-0396
Volume: 267
Issue: 5
Pages: 2792 - 2823
DOI: 10.1016/j.jde.2019.03.026
Type of Publication: A1 Journal article – refereed
Field of Science: 111 Mathematics
Subjects:
Funding: This work was supported by the Finnish Academy of Science and Letters, Väisälä Foundation. J. Ok was supported by the National Research Foundation of Korea funded by Korean Government (NRF-2017R1C1B2010328).