The maximal operator on generalized Orlicz spaces

By P. Hasto. 2015

127 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/8fc073c301f8fb9d080588964af5d89351d7ae22

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In Applied Mathematics

Citations in the corpus

Generalized Orlicz spaces and related PDE (2016, background): “With appropriate assumptions, the maximal operator is bounded in all t hese cases [19, 20].”
A borderline case of Calder\'on-Zygmund estimates for non-uniformly elliptic problems (2019, background): “Eventually, several contributions have been given in this direction, see for instance [12, 13, 14, 18, 19, 20, 24, 25, 29, 30, 31, 32] amongst the most closely related to the setting we are considering, that is the one of non-autonomous functionals with non-standard growth conditions.”
A pocket guide to nonlinear differential equations in Musielak–Orlicz spaces (2018, background): “Nowadays intensively investigated fields are also potential theory [115], harmonic analysis [72, 121], regularity theory [116, 120], and homogenization within the setting is studied in [39, 40].”
Hölder regularity of quasiminimizers under generalized growth conditions (2017, methodology): “Assume following [24] that there exist β, σ > 0 such that φ(β) 6 1 6 φ−(σ) and φ+B(βt) 6 φ − B(t) when t ∈ [ σ, (φB) −1( 1 |B|) ] for every ball B ⊂ Ω.”
Recent developments in problems with nonstandard growth and nonuniform ellipticity (2021, background): “For instance, in [130] Hästo has proved the boundedness of the classical Hardy-Littlewood Maximal operator”
Extrapolation and interpolation in generalized Orlicz spaces (2018, methodology): “The second author and his collaborators [30, 31, 34, 35] have systematically studied these questions and established a very broad theory that unites and extends previous work.”
Regularity for general functionals with double phase (2017, background): “13) F (x, v, z) ≈ Φ(x, |z|) and Φ(·) is a generalized Young function in the sense specified for instance in [19, 32].”
On the Regularity of Minima of Non-autonomous Functionals (2019, unknown): “For this we refer to [36–39, 50].”